2023
D. Lacker, K. Ramanan and R. Wu, “Local weak convergence for Large networks of interacting processes, “Annals of Applied Probability, Vol. 33, Number 2 (2023) 643-688, [Arvix, 2020].
C. Aistleitner, N. Gantert, Z. Kabluchko, J. Prochno and K. Ramanan
Large deviation principles for lacunary sums, “Transactions of the AMS, Vol. 376, Number 1 (2023) 507-553 [Arxiv, 2020].
2022
S S Kim, Y-T Liao and K Ramanan
An asymptotic thin shell condition and large deviations for multidimensional projections
Advances in Applied Mathematics, vol. 134, 102306 (2022)
P Dupuis and Y Mao
Formulation and properties of a divergence used to compare probability measures without absolute continuity
J Birrell, P Dupuis, M A Katsoulakis, Y Pantazis, L Rey-Bellet
(f,Gamma)-Divergences: Interpolatin between f-divergences and integral probability metrics
P Dupuis and G S Medvedev
The large deviation principle for interacting dynamical systems on random graphs
2021
S V Lototsky, R Mikulevicius and B L Rozovsky
Intrusive and non-instrusive chaos approximation for a two-
dimensional steady state Navier-stokes system with random forcing.
R Atar, A Budhiraja, P Dupuis, and R Wu
Large Deviations for the Single-Server Queue and the Reneging Paradox
P Dupuis and G-J Wu
Large Deviation Properties of the E mpirical Measure of a Metastable Small Noise Diffusion
A Budhiraja, P Dupuis, P Nyquist, G-J Wu
Quasistationary distributions and ergodic control problems
J Birrell, P Dupuis, M A Katsoulakis, L Rey-Bellet and J Wang
Variational Representations and Neural Network Estimation of Renyi Divergences
2020
D. Lacker, K. Ramanan and R. Wu, “Local weak convergence for Large networks of interacting processes, “Annals of Applied Probability, Vol. 33, Number 2 (2023) 643-688, [Arvix, 2020].
C. Aistleitner, N. Gantert, Z. Kabluchko, J. Prochno and K. Ramanan
Large deviation principles for lacunary sums, “Transactions of the AMS, Vol. 376, Number 1 (2023) 507-553 [Arxiv, 2020].
J Klobusicky, G Menon and R L Pego
Two-dimensional grain boundary networks: stochastic particle models and kinetic limits.
Paul Dupius and Gjou-Jhen Wu
Large deviation properties of the empirical measure of a stochastic differential equation with small noise.
Rami Atar, Amarjit Budhiraja, Paul Dupuis and Ruoyu Wu
Robust bounds and optimization at the large deviations scale for queueing models via R\’enyl divergence.
Hongjie Dong and Doyoon Kim
Lp-estimates for time fractional parabolic equations in divergence form with measurable coefficients.
Hongjie Dong and Qi S. Zhang
Time analyticity for the heat equation and Navier-Stokes Equations.
Hongjie Dong and Chiara Gallarati
Higher-Order Parabolic Equations with VMO Assumptions and General Boundary Conditions with Variable Leading Coefficients.
Hongjie Dong and Zongyuan Li
Classical Solutions of Oblique Derivative Problem in Nonsmooth Domains with Mean Dini Coefficients.
Hongjie Dong and Kunrui Wang
Boundary e-Regularity Criteria for the Three-Dimensional Navier-Stokes Equations.
C. Dafermos
Wave scattering in hyperbolic balance laws and the zero relaxation limit.
A Volkening, MR Abbott, N Chandra, B Dubois, F Lim, D Sexton, and B Sandstede
Modeling stripe formation on growing zebrafish tailfins.
MR McGuirl, SP Smith, B Sandstede, and S Ramachandran
Detecting shared genetic architecture among multiple phenotypes by hierarchical clustering of gene-level association statistics.
JJ Bramburger and B Sandstede
Localized patterns in planar bistable weakly coupled lattice systems.
R Parker, PG Kevrekidis, and B Sandstede
Existence and spectral stability of multi-pulses in discrete Hamiltonian lattice systems.
JJ Bramburger and B Sandstede
Spatially localized structures in lattice dynamical systems.
MR McGuirl, A Volkening, and B Sandstede
Topological data analysis of zebrafish patterns.
S. V. Lototsky and B. L. Rozovsky
Classical and generalized solutions of fractional stochastic differential equations.
2019
Shankar Bhamidi, Amarjit Budhiraja, Paul Dupuis and Ruoyu Wu
Rare event asymptotics for exploration processes for random graphs.
Jeremiah Birrell, Paul Dupuis, Markos A. Katsoulakis, Luc Rey-Bellet, and Jie Wang
Distributional Robustness and Uncertainty Quantification for Rare Events.
Rami Atar, Amarjit Budhiraja, Paul Dupuis, and Ruoyu Wu
Large Deviations for the Single Server Queue and the Reneging Paradox
Amarjit Budhiraja and Paul Dupuis
Analysis and Approximation of Rare Events: Representations and Weak Convergence Methods
Amarjit Budhiraja and Paul Dupuis
Recursive Markov Systems with Small Noise.
Amarjit Budhiraja and Paul Dupuis
Relative Entropy and Tightness of Measures
Amarjit Budhiraja and Paul Dupuis
Stochastic Flows of Diffeomorphisms and Image Matching.
Amarjit Budhiraja and Paul Dupuis
Models with Special Features
Amarjit Budhiraja and Paul Dupuis
Examples of Representations and Their Application
Amarjit Budhiraja and Paul Dupuis
Rare Event Mote Carlo and Importance Sampling
Amarjit Budhiraja and Paul Dupuis
Large and Moderate Deviations for Finite Dimensional Systems.
Amarjit Budhiraja and Paul Dupuis
Representations for Continuous Time Processes.
Amarjit Budhiraja and Paul Dupuis
Multilevel Splitting
Amarjit Budhiraja and Paul Dupuis
Systems Driven by an Infinite Dimensional Brownian Noise
Amarjit Budhiraja and Paul Dupuis
Moderate Deviations for Recursive Markov Systems
Amarjit Budhiraja and Paul Dupuis
Models with Special Features
Amarjit Budhiraja and Paul Dupuis
General Theory
Amarjit Budhiraja and Paul Dupuis
Abstract Sufficient Conditions for Large and Moderate Deviations in the Small Noise Limit
Amarjit Budhiraja and Paul Dupuis
Performance of an IS Scheme Based on a Subsolution
Amarjit Budhiraja and Paul Dupuis
Empirical Measure of a Markov Chain
Paul Dupuis, Vaios Laschos and Kavita Ramanan
Exit time risk-sensitive control for systems of cooperative agents
Paul Dupuis, Guo-jhen Wu, and Michael Snarski
Infinte Swapping using IID Samples
CM Dafermos
Uniqueness of Zero Relaxation Limit.
SIAM Journal on Mathematical Analysis 51 (3), 1999-2018
Hongjie Dong and Longjuan Xu
Hessian Estimates for Non-divergence form Elliptic Equations Arising from Composite Materials
Hongjie Dong and Doyoon Kim
Lp-estimates for time fractional parabolic equations with coefficients measurable in time.
Jongkeun Choi and Hongjie Dong
Gradient estimates for Stokes systems with Dini Mean oscillation coefficients.
Hongjie Dong and Longjuan Xu
Gradient estimates for divergence form elliptic systems arising from composite material.
Hongjie Dong, Tong Yang and Mingying Zhong
Exterior problem of the linear Vlasov-Poisson-Boltzmann System.
Jongkeun Choi, Hongjie Dong and Zhongyuan Li
Optimal Regularity for a Dirichlet-Conormal Problem in Reifenberg Flat Domain
Hongjie Dong and N. V. Kkrylov
Fully nonlinear elliptic and parabolic equations in weighted and mied-norm Sobolev spaces.
Hongjie Dong and Haigang Li
Optimal estimates for the conductivity probem by Green’s Function Method
Hongjie Dong and Hong Zhang
On Schauder estimates for a class of nonlocal fully nonlinear parabolic equations
Jongjeun Choi and Hongjie Dong
Gradient estimates for Stokes systems in domains
Hongjie Dong and Seick Kim
Partial Schauder Estimates for Second-Order Elliptic and Parabolic Equations: A revisit
Hongjie Dong and Doyoon Kim
Lq-Estimates for stationary Stokes system with coefficients measurable in one direction
C. Dafermos
Uniqueness of zero relaxation limit”
SIAM J. Math. Anal., 51 (2019), 1999-2018.
S Dodson and B Sandstede
Determining the source of period-doubling instabilities in spiral waves.
X. Cao, B. Sandstede, and X Luo
A functional data method for causal dynamic network modeling of task-related fMRI.
W. Strauss, A. Constantin and E. Varvaruca
Large-amplitude steady downstreamwater waves.
W. Strauss and Y. Wu
Rapidly rotating stars.
W. Strauss and J. Jang and Y. Wu
Existence of rotating magnetic stars.
S Iyer and B Sandstede
Mixing in reaction-diffusion systems: large phase offsets.
T Aougab, M Beck, P Carter, S Desai, B Sandstede, M Stadt, and A Wheeler
Isolas versus snaking of localized rolls.
Cao, B Sandstede, and X Luo
A functional data method for causal dynamic network modeling of task-related fMRI.
2018
M. V. Ciocanel, B. Sandstede, S. P. Jeschonek and K. L. Mowry
Modeling microtubule-based transport and anchoring of mRNA.
Hongjie Dong and Doyoon Kim
On Lp-Estimates for Elliptic and Parabolic Equations with Ap Weights.
Hongjie Dong and Seick Kim
Fundamental Solutions for Second-Order Parabolic Systems with Drift Terms.
Hongjie Dong, Luis Escauriaza and Seick Kim
On C1, C2, and weak type-(1, 1) estimates for linear elliptic operators: Part II.
Jongkeun Choi, Hongjie Dong and Doyoon Kim
Green Functions of Cornmal Derivative Problems for Stationary Stokes System
Jongkeun Choi, Hongjie Dong and Doyoon Kim
Conormal Deriative Problems for Stationary Stokes System in Sobolev Spaces.
Hongjie Dong, Tianling Jin and Hong Zhang
Dini and Schauder Estimates for Nonlocal Fully Nonlinear Parabolic Equations with Drifts.
Hongjie Dong and Hong Zhang
Dini estimates for nonlocal fully nonlinear elliptic equations.
Hongjie Dong and Doyoon Kim
Weighted Lq-estimates for stationary Stokes system with partially BMO coefficients.
Hongjie Dong and Chiara Gallarati
Higher-order elliptic and parabolic equatios with VMO assumptions and general boundary conditions.
F. Delarue, D. Lacker and K. Ramanan
From the master equation to mean field game limit theory: Large deviations and concentration of measure.
Constantine Dafermos
Hyperbolic balance laws with dissipative source relaxing to adiabatic conservation laws.
B. L. Rozovsky and S. V. Lototsky
Classical and Generalized Solutions of Fractional Stochastic Differential Equations.
B. Rozovskii , T. Chen, and C.-W. Shu
Numerical solutions of stochastic PDEs driven by arbitrary type of noise.
B. L. Rozovsky and S. V. Lototsky
Stochastic Evolution Systems. Linear Theory and Applications to Non-linear Filtering.
W. Strauss and S. W. So
Upper bound on the slope of steady water waves with small adverse vorticity
E Makrides and B Sandstede
Existence and stability of spatially localized patterns.
HM McNamara, S Dodson, Y-L Huang, EW Miller, B Sandstede, and AE Cohen
Geometry-dependent instabilities in electrically excitable tissues.
B de Rijk and B Sandstede
Diffusive stability against nonlocalized perturbations of planar wave trains in reaction-diffusion systems.
A Volkening and B Sandstede
Iridophores as a source of robustness in zebrafish stripes and variability in Danio patterns.
P Carter and B Sandstede
Unpeeling a homoclinic banana in the FitzHugh-Nagumo system.
B Barker, R Nguyen, B Sandstede, N Ventura, and C Wahl
Computing Evans functions numerically via boundary-value problems.
C M Dafermos
Hyperbolic balance laws with dissipative source relaxing to adiabatic conservation laws.
2017
Paul Dupuis, J. Doll and P. Nyquist
Thermodynamic integration methods, infinite swapping and the calculation of generalized averages.
J Klobusicky, G Menon
Concentration inequalities for a removal-driven thinning process.
Paul Dupuis, J. Doll and P. Nyquist
A large deviations analysis of certain qualitative properties of parallel tempering and infinite swapping algorithms.
P. Dupuis and D. Johnson
Moderate deviations based importance sampling for stochastic recursive equations
B. L. Rozovsky and S. Lototsky
Stochastic Partial Differential Equations.
W. Strauss and Y. Wu
Steady states of rotating stars and galaxies.
V Ciocanel, JA Kreiling, JA Gagnon, KL Mowry, and B Sandstede
Analysis of active transport by fluorescence recovery after photobleaching.
C Xia, C Cochrane, J DeGuire, G Fan, E Holmes, M McGuirl, P Murphy, J Palmer, P Carter, L Slivinski, and B Sandstede
Assimilating Eulerian and Lagrangian data in traffic-flow models.
2016
D Johnson-Chyzhykov and G Menon
The building game: from enumerative combinatorics to conformational diffusion
E. Russell and G Menon
Energy landscapes for the self-assembly of supramolecular polyhedra
G. Menon
The Airy function is a Fredholm determinant
G Menon and T Trogdon
Smoothed analysis for the conjugate gradient algorithm, SIGMA, 12 (2016)
R Abgrall, CW Shu, C Dafermos, EF Toro, TH Sonar, F Coquel, B Despres, et al.
Handbook of Numerical Methods for Hyperbolic Problems, Vol 17. Handbook of Numerical Analysis
CM Dafermos
Hyperbolic balance laws with relaxation
CM Dafermos
BV Solutions for Systems of Balance Laws
CM Dafermos
Steady and Self-Similar Solutions in Multi-Space Dimensions
CM Dafermos
Scalar Conservation Laws in One Space Dimension
CM Dafermos
Construction of BV Solutions by the Vanishing Viscosity Method
CM Dafermos
The Cauchy Problem
CM Dafermos
Admissible Wave Fans and the Riemann Problem
CM Dafermos
Admissible Shocks
CM Dafermos
The L1 Theory for Scalar Conservation Laws
CM Dafermos
Entropy and the Stability of Classical Solutions
Hyperbolic Conservation Laws in Continuum Physics
CM Dafermos
BV Solutions for Hyperbolic Balance Laws with periodic initial data
Constantine Dafermos
BV solutions for hyperbolic balance laws with periodic initial data.
CM Dafermos
Introduction to the theory of hyperbolic conservation laws
Paul Dupuis, M. A. Katsoulakis, Y. Pantazis and P. Plechac
Path-space information bounds for uncertainty quantification and sensitivity analysis of stochastic dynamics.
R. Abgrall and Chi-Wang Shu (eds.) North Holland
Introduction to the Theory of Hyperbolic Conservation Laws.
Handbook of Numerical Analysis.
B. Rozovsky and R. Mikulevicius
On distribution free Skorokhod- Malliavin Calculus.
B. Rozovsky, G. E. Karniadakis, and Z. Zhang
Strong and weak convergence rate of finite element methods for semi-linear equations with additive white noise.
W. Strauss, A. Constantin and E. Varvaruca
Global bifurcation of steady gravity water waves with critical layers.
W. Strauss and M. Wheeler
Bound on the slope of steady water waves with favorable vorticity.
W. Strauss, D. Ambrose and D. Wright
Global bifurcation theory for periodic traveling interfacial gravity-capillary waves with critical layers.
W. Strauss and X. Chen
Convergence to equilibrium of a body moving in a kinetic sea.
P Carter, B de Rijk, and B Sandstede
Stability of traveling pulses with oscillatory tails in the FitzHugh-Nagumo system.
EA Powrie, V Ciocanel, JA Kreiling, JA Gagnon, B Sandstede, and KL Mowry
Using in vivo imaging to measure RNA mobility in Xenopus laevis oocytes.
2015
Paul Dupuis, A. Budhiraja, M. Rischer and K. Ramanan
Limits of relative entropies associated with weakly interacting particle systems.
B. Rozovsky, M Zheng, and G. E. Karniadakis
Adaptive Wick-Malliavin Approximation to Nonlinear SPDEs with Discrete random Variables.
W. Strauss, T. T. Nguyen, and T. V. Nguyen
Global magnetic confinement for the 1.5 D Vlasov-Maxwell system.
W. Strauss, E. Esenturk and H. J. Hwang
Stationary solutions of the Vlasov-Poisson system with diffusive boundary conditions.
W. Strauss and Xuwen Chen
Velocity reversal criterion of a body immersed in a sea of particles.
B Sandstede and T Theerakarn
Regularity of center manifolds via the graph transform.
A Volkening and B Sandstede
Modelling stripe formation in zebrafish: an agent-based approach.
J Guckenheimer, B Krauskopf, HM Osinga and B Sandstede
Invariant manifolds and global bifurcations.
P Carter and B Sandstede
Fast pulses with oscillatory tails in the FitzHugh-Nagumo system.
L Slivinski, E Spiller, A Apte, and B Sandstede
A hybrid particle-ensemble Kalman filter for Lagrangian data assimilation.
2014
B. Rozovskii, Z. Zhang, M. V. Tretyakov, and G. E. Karniadakis
Wiener chaos vs stochastic collocation methods for linear advection-diffusion quations with multiplicative white noise.
W. Strauss and Xuwen Chen
Approach to equilibrium of a body colliding specularly and diffusely with a sea of particles.
W. Strauss and T. Nguyen
Linear stability analysis of a hot plasma in a solid torus.
P Carter, PL Christiansen, YB Gaididei, C Gorria, B Sandstede, MP Sorensen, and J Starke
Multi-jam solutions in traffic models with velocity-dependent driver strategies.
K McQuighan and B Sandstede
Oscillons in the planar Ginzburg-Landau equation with 2:1 forcing.
M Beck, T Nguyen, B Sandstede and K Zumbrun
Nonlinear stability of source defects in the complex Ginzburg-Landau equation.
P van Heijster and B Sandstede
Bifurcations to travelling planar spots in a three-component FitzHugh-Nagumo system.
E Makrides and B Sandstede
Predicting the bifurcation structure of localized snaking patterns.
Hongjie Dong and Seick Kim
Green’s functions for parabolic systems of second order in time-varying domains
Hongjie Dong and Jinggang Xiong
Boundary gradient estimates for parabolic and elliptic systems from linear laminates
Hongjie Dong
On a multi-dimensional transport equation with nonlocal velocity.
Hongjie Dong and Xumin Gu
Boundary partial regularity for the high dimensional Navier-Stokes equations.
Hongjie Dong and Doyoon Kim
On the impossibility of $W_p^2$ estimates for elliptic equations with piecewise constant coefficients.
Hongjie Dong and Doyoon Kim
Parabolic equations in simple convex polytopes with time irregular coefficients.
Hongjie Dong and Hong Zhang
Schauder estimates for higher-order parabolic systems with time irregular coefficients.
Govind Menon, D. Gracias, D. Johnson, R. Kaplan, J. Klobusicky, and S. Pandey
Self-assembly of mesoscale isomers: the role of pathways and degrees of freedom.
Govind Menon, P. Deift, S. Olver, and T. Trogdon
Universality in numerical computations with random data.
Govind Menon, D. Gracias, R. Kaplan, J. Klobusicky, and S. Pandey
Building polyhedra by self-assembly: theory and experiment.
Harold Kushner
A partial history of the early development of continuous-time nonlinear stochastic systems theory.
2013
W. Strauss and T. Nyugen
Stability analysis of collisionless plasmas with specularly reflecting boundary.
SIAM J. Math. Anal. 45 (2013), 777-808.
S McCalla and B Sandstede
Spots in the Swift-Hohenberg equation.
SIAM Journal on Applied Dynamical Systems 12 (2013) 831-877.
HJ Hupkes and B Sandstede
Stability of pulse solutions for the discrete FitzHugh-Nagumo system.
Transactions of the American Mathematical Society 365(2013) 251-301.
Hongjie Dong and N. V. Krylov
On the existence of smooth solutions for fully nonlinear parabolic equations with measurable “coefficients” without convexity assumptions
Comm. Partial Differential Equations, 38 (2013), no. 6, 1038–1068
Hongjie Dong and Doyoon Kim
Schauder estimates for a class of nonlocal elliptic equations
Discrete Contin. Dyn. Syst.-A 33 (2013) no. 6, 2319-2347
Hongjie Dong and Dong Li
Global $\dot H^1 \cap \dot H^{-1}$ solutions to a logarithmically regularized 2D Euler equation
J. Math. Fluid Mech., 2013
Hongjie Dong and Dong Li
On a one-dimensional $\alpha$-patch model with nonlocal drift and fractional dissipation
Trans. Amer. Math. Soc., 366 (2014), no. 4, 2041–2061
Hongjie Dong
On elliptic equations in a half space or in convex wedges with irregular coefficients
Adv. Math., 238 (2013), 24–49
Hongjie Dong and Dong Li
On a generalized maximum principle for a transport-diffusion model with log-modulated fractional dissipation
Discrete Contin. Dyn. Syst.-A 34 (2013), no.9, 3437–3454
Govind Menon, with Andrew Sageman-Furnas, Parikshit Goswami and Stephen Russell
The Sphereprint: An approach to quantifying the conformability of flexible materials.
Journal of Textile Research, (2013).
Govind Menon, with Helen Li.
Numerical solution of Dyson Brownian motion and a sampling scheme for invariant matrix ensembles.
J. Stat. Phys. Vol 153, (2013).
Govind Menon, with C. Pfrang and Percy Deift
How long does it take to compute the eigenvalues of a random symmetric matrix?
Featured in MSRI volume on random matrix theory.
Paul Dupuis and Y. Cai
Analysis of an interacting particle method for rare event estimation.
Queueing Systems 73(4), April 2013.
2012
W. Strauss
Vorticity jumps in steady water waves.
Disc. Cont. Dyn. Sys.-B 17 (2012), 1101-1113
B Sandstede and Y Xu
Snakes and isolas in non-reversible conservative systems.
Dynamical Systems 27 (2012) 317-329.
P van Heijster and B Sandstede
Coexistence of stable spots and fronts in a three-component FitzHugh-Nagumo system.
RIMS Kokyuroku Bessatsu B31 (2012) 135-155.
B Sandstede, A Scheel, G Schneider and H Uecker
Diffusive mixing of periodic wave trains in reaction-diffusion systems.
Journal of Differential Equations 252 (2012) 3541-3574.
M Beck, T Nguyen, B Sandstede and K Zumbrun
Toward nonlinear stability of sources via a modified Burgers equation.
Physica D 241 (2012) 382-392.
Constantine Dafermos
Maximal dissipation in equations of evolution
J. Diff. Equations 252 (2012), 567-587
Constantine Dafermos
N-waves in hyperbolic balance laws.
Journal of Hyperbolic Equations, 9, 2, 339-354, 2012.
Constantine Dafermos
Hyperbolic Conservation Laws: Analytical Properties
Encyclopedia of Applied and Computational Mathematics. B. Engquist (ed.) Springer-Verlag, Berlin.
Constantine Dafermos
Regularity of solutions to the equations of thermoelasticity
Encyclopedia of Thermal Stresses. R. Hetnarski (ed.) Springer-Verlag, Berlin.
Hongjie Dong
Solvability of second-order equations with hierarchically partially BMO coefficients
Trans. Amer. Math. Soc., 364 (2012) no. 1, 493–517
Hongjie Dong, N. V. Krylov and X. Li
On fully nonlinear elliptic and parabolic equations in domains with VMO coefficients
Algebra i Analis (St. Petersburg Math. J.), 24 (2012) no. 1
Paul Dupuis, Y. Liu, N. Plattner and J. D. Doll
On the infinite swapping limit for parallel tempering
Paul Dupuis, K. Spiliopoulos and H. Wang
Importance sampling for multiscale diffusions
SIAM J. on Multiscale Modeling and Simulation, 10 (1) 1 – 27, 2012.
Paul Dupuis, B. Kaynar, A. Ridder, R. Rubinstein and Radislav Vaisman
Counting with combined splitting and capture-recapture methods
Paul Dupuis and K. Chowdhary
Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification
ESAIM: Mathematical Modeling and Numerical Analysis
Paul Dupuis and K. Spiliopoulos
Large deviations for multiscale diffusions via weak convergence methods
Stochastic Processes and Their Applications, 122(4), 2010.
Paul Dupuis and M. Fischer
On the construction of Lyapunov functions for nonlinear Markov processes via relative entropy
Paul Dupuis, A. Budhiraja and M. Fischer
Large deviation properties of weakly interacting processes via weak convergence methods
Justin Holmer (with Quanhui Lin)
Phase-driven interaction of widely separated nonlinear Schroedinger solitons
Justin Holmer (with Svetlana Roudenko)
Blow-up solutions on a sphere for the 3d quintic NLS in the energy space
Analysis and PDE
Justin Holmer
Dynamics of KdV solitons in the presence of a slowly varying potential
Harold Kushner
Modeling and Approximations for Stochastic Systems with State-Dependent Singular Controls and Wide-Band Noise
2012 IEEE CDC Conference on Decision and Control
Harold Kushner
Controlled Nonlinear Stochastic Delay Equations: Part I: Modeling and Approximations
Applied Math and Optimization, Vol. 66, 2012, pages 77-54
Harold Kushner
Controlled Nonlinear Stochastic Delay Equations: Part II: Approximations and Pipe-Flow Representations
Applied Math and Optimization, Vol. 66, 2012, pages 55-80
Govind Menon, (in honor of Constantine Dafermos)
Lesser known miracles of Burgers equation
Acta Mathematica Scientia, Vol. 32 (2012)
Govind Menon
Complete integrability of shock clustering and Burgers turbulence
Arch. Rational Mech. Anal. Vol. 203, (2012).
Govind Menon with M. Hadzic
Gradient flow structure for domain relaxation in Langmuir Films
Q. App. Math. Vol. 70 (2012).
B Sandstede, A Scheel, G Schneider and H Uecker
Diffusive mixing of periodic wave trains in reaction-diffusion systems
Journal of Differential Equations (2012)
P van Heijster and B Sandstede
Coexistence of stable spots and fronts in a three-component Fitzhugh-Nagumo system
RIMS Kokyuroku Bessatsu, (2012), B31, 135-155.
HJ Hupkes and B Sandstede
Stability of pulse solutions for the discrete FitzHugh-Nagumo system
Transactions of the American Mathematical Society (2012).
M Beck, T Nguyen, B Sandstede and K Zumbrun
Toward nonlinear stability of sources via a modified Burgers equation
Physica D 241 (2012) 382-292
Harold Kushner
Controlled Nonlinear Stochastic Delay Equations: Part II: Approximations and Pipe-Flow Representations
Appl Math Optim (2012) 66:55-80
2011
W. Strauss and A. Constantin
Periodic traveling gravity waves with discontinuous vorticity.
Arch. Rat. Mech. Anal. 202 (2011), 133-175.
P van Heijster and B Sandstede
Planar radial spots in a three-component FitzHugh-Nagumo system.
Journal of Nonlinear Science 21 (2011) 705-745.
HJ Hupkes, D Pelinovsky and B Sandstede
Propagation failure in the discrete Nagumo equation.
Proceedings of the American Mathematical Society 139(2011) 3537-3551.
J Knobloch, DJB Lloyd, B Sandstede and T Wagenknecht
Isolas of 2-pulse solutions in homoclinic snaking scenarios.
Journal of Dynamics and Differential Equations 23(2011) 93-114.
G Derks, S Maad and B Sandstede
Perturbations of embedded eigenvalues for the planar bilaplacian.
Journal of Functional Analysis 260 (2011) 340-398.
Constantine Dafermos
Generalized characteristics and the Hunter-Saxton equation
Journal of Hyperbolic Equations, 8 (2011), 159-168
Hongjie Dong
The aggregation equation with power-law kernels: ill-posedness, mass concentration and similarity solutions
Comm. Math. Phys. 304 (2011) no. 3, 649–664
Hongjie Dong and D. Kim
Parabolic and elliptic systems in divergence form with variably partially BMO coefficients.
SIAM J. Math. Anal., 43 (2011) no. 3, 1075–1098
Hongjie Dong and D. Kim
Global regularity of weak solutions to quasilinear elliptic and parabolic equations with controlled growth
Comm. Partial Differential Equations, 36 (2011) no. 10, 1750–1777
Hongjie Dong, S. Cho and S. Kim
Global estimates for Green’s matrix of second order parabolic systems with application to elliptic systems in two dimensional domains
Potential Anal. (2011)
Hongjie Dong
On similarity solutions to the multidimensional aggregation equation
SIAM J. Math.Anal., 43 (2011) no. 4, 1995–2008
Hongjie Dong and D. Kim
Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains
J. Funct. Anal., 261 (2011) no. 11, 3279–3327
Hongjie Dong and D. Kim
On Lp-estimates for a class of nonlocal elliptic equations
J. Funct. Anal., (2011), doi:10.1016/j.jfa.2011.11.002
Hongjie Dong
Parabolic equations with variably partially VMO coefficients
Algebra i Analis (St. Petersburg Math. J.) 23 (2011) no.3, 150–174
Hongjie Dong and S. Kim
Partial Schauder estimate for second-order elliptic and parabolic equations
Calc. Var. Partial Differential Equations, 40 (2011) no. 3–4, 481–500
Hongjie Dong and D. Li
On the 2D critical and supercritical dissipative quasi-geostrophic equation in Besov spaces
J. Differential Equations 248 (2010), no. 11, 2684–2702
Hongjie Dong and D. Kim
Lp solvability of divergence type parabolic and elliptic systems with partially BMO coefficient
Calc. Var. Partial Differential Equations 40 (2011) no. 3–4, 357–389
Hongjie Dong and and D. Kim
On the Lp-solvability of higher order parabolic and elliptic systems with BMO coefficients
Arch. Rational Mech. Anal. 199 (2011) no. 3, 889–941
Paul Dupuis, N. Plattner, J. D. Doll, H. Wang, Y. Liu, and J. Gubernatis
An infinite swapping approach to the rare-event sampling problem
J. of Chemical Physics, 135, (2011), 134111
Paul Dupuis, A. Budhiraja and V. Maroulas
Variational representations for continuous time processes
Annales de l.Institut Henri Poincaré, 47, (2011), 725-747
Paul Dupuis and T. Dean
The design and analysis of a generalized RESTART/DPR algorithm for rare event simulation
Annals of OR, 189, (2011), 63-02
Yan Guo and I. Tice
Rayleigh-Taylor instability for compressible inviscid fluids
Indiana University Math. (2011)
Yan Guo, R. Esposito and R. Marra
Validity of the Boltzmann equation with an external field
Kinet. Relat. Models 4 (2011), no. 2, 499-515
Yan Guo and B. Pausader
Global smooth ion dynamics in the Euler-Poisson system
Commun. Math. Phys. 303 (2011), no. 1, 89-125
Yan Guo and T. Nguyen
A note on Prandtl layer problem
Comm. Pure Appl. Math., 64, (2011) no. 10, 1416-1438
Yan Guo and R. Strain
Momentum regularity and stability of the relativistic Vlasov-Maxwell-Boltzmann system
Commun. Math. Phys. (2011)
Yan Guo
The Vlasov-Poisson-Landau system in a periodic box
Journal of AMS (2011)
Justin Holmer (with Galina Perelman and Maciej Zworski, and an appendix by Bernd Sturmfels)
Effective dynamics of double solitons for perturbed mKdV
Communications in Mathematical Physics 305 (2011) pp. 363-425
Justin Holmer and Svetlana Roudenko
A class of solutions to the 3d cubic nonlinear Schroedinger equation that blow-up on a circle
AMRX Appl Math Res Express 2011 (1): 23-94
HJ Hupkes, D Pelinovsky and B Sandstede
Propagation failure in the discrete Nagumo equation
Proceedings of the American Mathematical Society 139 (2011) 3537-3551
J Knobloch, DJB Lloyd, B Sandstede and T Wagenknecht
Isolas of 2-pulse solutions in homoclinic snaking scenarios
Journal of Dynamics and Differential Equations 23 (2011) 93-114
Harold Kushner
Numerical Methods for Stochastic Singular Control Problems with State-Dependent Control
SIAM J on Control and Optimization
Harold Kushner
Numerical Methods for Controls for Nonlinear Stochastic Systems With Delays and Jumps: Applications to Admission Control
Stochastics: An International Journal of Probability and Statistics, Vol. 83, 2011, pages 277-310
John Mallet-Paret and R. D. Nussbaum
Inequivalent measures of noncompactness and the Radius of the Essential Spectrum
Proc. Amer. Math. Soc. 139 (2011), pp. 917–930
John Mallet-Paret and R. D. Nussbaum
Inequivalent measures of noncompactness
Annali di Matematica 190 (2011), pp. 453–488
John Mallet-Paret and R. D. Nussbaum
Superstability and rigorous asymptotics in singularly perturbed state-dependent delay differential equations
J. Diff. Eq. 250 (2011), pp. 4037–4084
Govind Menon, with S. Pandey, M. Ewing, D. Kunas, N. Hguyan and D. Gracias
Algorithmic design of self-folding polyhedra.
PNAS ( Oct. 28, 2011).
Weining Kang and Kavita Ramanan
Characterization of Stationary Distributions of Reflected Diffusions
P van Heijster and B Sandstede
Planar radial spots in a three-component FitzHugh-Nagumo system
Journal of Nonlinear Science 21 (2011) 705-745
Hui Wang, N. Plattner, J. Doll, P. Dupuis, Y. Liu, and J. E. Gubernatis
An infinite swapping approach to the rare-event sampling problem
J. Chem. Phys. 135, 134111, 2011
Hui Wang, P. Dupuis and K. Spiliopoulos
Rare event simulation for rough energy landscapes
Proceeding of the 2011 Winter Simulation Conference, 2011
Hui Wang and L. Setayeshgar
Large deviations for a feedforward network
Adv. Appl. Prob. 43, 545-571, 2011
2010
W. Strauss and A. Constantin
Trochoidal solutions to the incompressible two-dimensional Euler equations.
J. Math. Fluid Mech. 12 (2010), 181-201.
W. Strauss, D. Ambrose, M. Lopes Filho and H. Nussenzveig Lopes
Transport of interfaces with surface tension by 2D viscous flows.
Interfaces and Free Boundaries 12 (2010), 23-44.
W. Strauss and A. Constantin
Pressure and trajectories beneath a Stokes wave.
Comm. Pure Appl. Math. 63 (2010), 533-557.
W. Strauss
Steady water waves.
Bull. AMS. 47 (2010), 671-694.
HJ Hupkes and B Sandstede
Travelling pulses for the discrete FitzHugh-Nagumo system.
SIAM Journal on Applied Dynamical Systems 9 (2010) 827-882.
D Avitabile, DJB Lloyd, J Burke, E Knobloch and B Sandstede
To snake or not to snake in the planar Swift-Hohenberg equation.
SIAM Journal on Applied Dynamical Systems 9 (2010) 704-733.
S McCalla and B Sandstede
Snaking of radial solutions of the multi-dimensional Swift-Hohenberg equation: a numerical study.
Physica D 239 (2010) 1581-1592.
D Obeid, JM Kosterlitz and B Sandstede
State selection in the noisy stabilized Kuramoto-Sivashinsky equation.
Physical Review E 81 (2010) 066205.
M Beck, B Sandstede and K Zumbrun
Nonlinear stability of time-periodic viscous shocks.
Archive for Rational Mechanics and Analysis 196 (2010) 1011-1076.
M Beck, HJ Hupkes, B Sandstede and K Zumbrun
Nonlinear stability of semidiscrete shocks for two-sided schemes.
SIAM Journal on Mathematical Analysis 42 (2010) 857-903.
M Oh and B Sandstede
Evans functions for periodic waves on infinite cylindrical domains.
Journal of Differential Equations 248 (2010) 544-555.
W.H.Fleming, H. Kaise and S-J. Sheu
Max-plus Stochastic Control and Risk Sensitivity
W.H. Fleming and D. Hernandez-Hernandez
On the Value of Stochastic Differential Games
Harold Kushner
Numerical Methods for the Optimization of Nonlinear Stochastic Delay Systems, and an Application to Internet Regulation
Proceedings of the 49th Conference on Decision and Control, 2010, IEEE Press, New York
Govind Menon
A kinetic theory of shock clustering in scalar conservation laws
Oberwolfach Reports Vol 7, Issue 3, (2010).
Govind Menon with R. Srivivasan
Kinetic theory and Lax equations for shock clustering and Burgers turbulence
J. Stat. Phys. 140, (2010).
Govind Menon, B. Niethammer and R. Pego
Dynamics and self-similarity in min-driven clustering
Trans. AMS Vol. 362 (2010)
2009
W. Strauss and B. Pausader
Analyticity of the scattering operator for fourth-order nonlinear waves.
Disc. Cont. Dyn. Sys. 25 (2009), 617-625.
V Manukian, N Costanzino, CKRT Jones and B Sandstede
Existence of multi-pulses of the regularized short-pulse and Ostrovsky equations.
Journal of Dynamics and Differential Equations 21(2009) 607-622.
HJ Hupkes and B Sandstede
Modulated wave trains in lattice differential systems.
Journal of Dynamics and Differential Equations 21(2009) 417-485.
V Manukian and B Sandstede
Multi-hump pulses in systems with reflection and phase invariance.
Journal of Differential Equations 247 (2009) 1866-1898.
M Beck, J Knobloch, DJB Lloyd, B Sandstede and T Wagenknecht
Snakes, ladders, and isolas of localised patterns.
SIAM Journal on Mathematical Analysis 41 (2009) 936-972.
A Doelman, B Sandstede, A Scheel and G Schneider
The dynamics of modulated wave trains.
Memoirs of the American Mathematical Society, 199 (934) (2009).
M Beck, A Ghazaryan and B Sandstede
Nonlinear convective stability of traveling fronts near Turing and Hopf instabilities.
Journal of Differential Equations 246 (2009) 4371-4390.
BG Bale, N Kutz and B Sandstede
Optimizing waveguide array mode-locking for high-power fiber lasers.
IEEE Journal of Selected Topics in Quantum Electronics 15 (2009) 210-231.
DJB Lloyd and B Sandstede
Localized radial solutions of the Swift-Hohenberg equation.
Nonlinearity 22 (2009) 485-524.
Harold Kushner
Numerical Methods for Optimal Controls for Nonlinear Stochastic Systems With Delays: Algorithms and Data
IEEE Trans on Automatic Control, Vol. 55, 2010, pages 2170-2176
Harold Kushner
Large Deviations for Two-Time-Scale Diffusions, With Delays
2008
W. Strauss and J. Ko
Effect of vorticity on steady water waves.
J. Fluid Mech. 608 (2008), 197-215.
W. Strauss and Z. Lin
A sharp stability criterion for the Vlasov-Maxwell system.
Inventiones Math. 173 (2008), 497-546.
W. Strauss and J. Ko
Large-amplitude steady rotational water waves.
Eur. J. Mech. B Fluids 27 (2008), 96-109.
W. Strauss and P. Karageorgis
Instability of steady states for nonlinear wave and heat equations.
J. Diff. Eqns. 241 (2007), 184-205.
DJB Lloyd, B Sandstede, D Avitabile and AR Champneys
Localized hexagon patterns of the planar Swift-Hohenberg equation.
SIAM Journal on Applied Dynamical Systems 7 (2008) 1049-1100.
G Derks, S Maad and B Sandstede
Perturbations of embedded eigenvalues for the bilaplacian on a cylinder.
Discrete and Continuous Dynamical Systems A 21(2008) 801-821.
B Sandstede and A Scheel
Hopf bifurcation from viscous shock waves.
SIAM Journal on Mathematical Analysis 39 (2008) 2033-2052.
N Kutz and B Sandstede
Theory of passive harmonic mode-locking using waveguide arrays.
Optics Express 16 (2008) 636-650.
B Sandstede and A Scheel
Relative Morse indices, Fredholm indices, and group velocities.
Discrete and Continuous Dynamical Systems A 20(2008) 139-158.
Abdelkader Boucherif
Nonlocal Problems for Parabolic Inclusions
Abdelkader Boucherif, Zehour Benbouziane, and Sidi Mohamed Bouguima
Existence Result for Impulsive Third Order Periodic Boundary Value Problems
Hongjie Dong and Dong Li
Optimal local smoothing and analyticity rate estimates for the generalized Navier-Stokes equations
Comm. Math. Sci. (2008)
Hongjie Dong and Dong Li
Finite time singularities for a class of generalized surface quasi-geostropic equations
Proc. Amer. Math., 136 (2008), 2555–2563
Hongjie Dong and Seick Kim
Green’s matrices of second order elliptic systems with measurable coefficients in two dimensional domains
Trans. Amer. Math. Soc. (2008)
Hongjie Dong
Well-posedness for a transport equation with nonlocal velocity
J. Funct. Anal, (2008)
Hongjie Dong and Doyoon Kim
Parabolic and elliptic systems with VMO coefficients
Hongjie Dong and Natas Pavlovic
Regularity criteria for the dissipative quasi-geostrophic equations in Hölder spaces
Comm. Math. Phys. (2008)
Hongjie Dong and Nicolai V. Krylov
Second-order elliptic and parabolic equations with B(R2, VMO) coefficients
Hongjie Dong, Seick Kim and Mikhail Safonov
On uniqueness of boundary blow-up solutions of a class of nonlinear elliptic equation
Comm. Partial Differential Equations 33 (2008), no. 2, 177-188
Paul Dupuis and Thomas Dean
The design and analysis of a generalized DPR algorithm for rare event simulation
Yan Guo and Mahir Hadzic
Stability in the Stefan problem with surface tension (I)
Yan Guo and R. Strain
Decay for soft potentials near Maxwellian
Arch. Rational Mech. Anal., 187 no. 2, 287-339. (2008)
Yan Guo and H. Hwang
Pattern formation (I): The Keller-Segel model
JDE, (2008)
Yan Guo and Z. Lin
Unstable and stable galaxy models
Commun. Math. Phys. (2008)
Harold Kushner
Stochastic Approximation: A Survey
Brown University, November, 2008, PDF
Bjorn Sandstede, A. Doelman, A. Scheel and G. Schneider
The dynamics of modulated wave trains
Memoirs of the American Mathematical Society (2008)
Bjorn Sandstede, D. J. B. Lloyd, D. Avitabile and A.R. Champneys
Localized hexagon patterns of the planar Swift-Hohenberg equation
SIAM Journal on Applied Dynamical Systems 7 (2008) 1049-1100
PDFHexagon movie Ladder movie)
Bjorn Sandstede, G. Derks, and S. Maad
Perturbations of embedded eigenvalues for the bilaplacian on a cylinder
Discrete and Continuous Dynamical Systems A 21 (2008) 801-821
Bjorn Sandstede and A. Scheel
Hopf bifurcation from viscous shock waves
SIAM Journal on Mathematical Analysis 39 (2008) 2033-2052
B Sandstede and N. Kutz
Theory of passive harmonic mode-locking using waveguide arrays
Optics Express 16 (2008) 636-650
Bjorn Sandstede and A. Scheel
Relative Morse indices, Fredholm indices, and group velocities
Discrete and Continuous Dynamical Systems A 20 (2008) 139-158
Hui Wang and Paul Dupuis
Importance Sampling for Jackson Networks
Hui Wang, Paul Dupuis and Kevin Leder
Importance Sampling for Weighted-Serve-the-Longest-Queue
2007
W. Strauss and P. Karageorgis
Instability of steady states for nonlinear wave and heat equations.
J. Diff. Eqns. 241 (2007), 184-205.
W. Strauss and A. Constantin
Rotational steady water waves near stagnation
Phil. Trans. Roy. Soc. 365 (2007), 2227-2239.
W. Strauss and A. Constantin
Stability properties of steady water waves with vorticity.
Comm. Pure Appl. Math. 60 (2007), 911-950.
W. Strauss and Z. Lin
Linear stability and instability of relativistic Vlasov-Maxwell systems
Comm. Pure Appl. Math. 60 (2007), 724-787.
W. Strauss and Z. Lin
Nonlinear stability and instability of relativistic Vlasov-Maxwell systems.
Comm. Pure Appl. Math. 60 (2007), 789-837.
B Sandstede
Evans functions and nonlinear stability of travelling waves in neuronal network models.
International Journal of Bifurcation and Chaos 17 (2007) 2693-2704.
B Sandstede and A Scheel
Period doubling of spiral waves and defects.
SIAM Journal on Applied Dynamical Systems 6 (2007) 494-547.
A Ghazaryan and B Sandstede
Nonlinear convective instability of Turing-unstable fronts near onset: A case study.
SIAM Journal on Applied Dynamical Systems 6 (2007) 319-347.
JDM Rademacher, B Sandstede and A Scheel.
Computing absolute and essential spectra using continuation.
Physica D 229 (2007) 166-183
Hongjie Dong and Dapeng Du
Global well-posedness and a decay estimate for the critical quasi-geostrophic equation
Discrete Contin. Dyn. Syst., Vol. 21, 4, (2008)
Hongjie Dong, Sungwon Cho and Seick Kim
On the fundamental solutions for strongly parabolic systems of second order
Hongjie Dong and N. Pavlovic
A regularity criterion for the dissipative quasi-geostrophic equations.
Amarjit Budhiraja, Paul Dupuis, and Vasileios Maroulasz
Large Deviations for Stochastic Flows of Diffeomorphisms.
Paul Dupuis, Kevin Leder, and Hui Wang
Large deviations and importance sampling for a tandem network with slow-down
Paul Dupuis, Kevin Leder and Hui Wang
On the Large Deviations Properties of the Weighted-Serve-the-Longest-Queue Policy
Progress in Probability
Thomas Dean, and Paul Dupuis
Splitting for Rare Event Simulation: A Large Deviations Approach to Design and Analysis
Amarjit Budhiraja, Paul Dupuis, and Vasileios Maroulas (March 2007)
Large Deviations for Infinite Dimensional Stochastic Dynamical Systems
Yan Guo and G. Rein
A non-variational approach to nonlinear stability in stellar dynamics applied to the King model
Commun. Math. Phys., 271 (2007) 489-509
Yan Guo, C. Hallstrom and D. Spirn
Dynamics near unstable, interfacial fluids
Commun. Math. Phys., 270 (2007), 635-689
Yan Guo and H. Hwang
Pattern formation (II): The Turing instability
Proc. AMS, 135 (2007), 2855-2866
Henrik Hult and Gennady Samorodnitsky
Tail probabilities for infinite series of regularly varying random vectors
Harold J. Kushner
Numerical Approximations to Optimal Nonlinear Filters
S. V. Lototsky and B. L. Rozovskii
Stochastic Partial Differential Equations Driven by Purely Spatial Noise
Submitted to SIAM Journal on Mathematical Analysis, 2007
S. V. Lototsky and B. L. Rozovskii
Stochastic Parabolic Equations of Full Second-Order
Book chapter in ” Topics in Stochastic Analysis and Nonparametric Estimation,” Ed. P.- L. Chow et al., 199-210,
The IMA Volumes in Mathematics and its Applications, Springer, 2007
S. V. Lototsky and B. L. Rozovskii
A Unified Approach to Stochastic Evolution Equations Using the Skorokhod Integral
Submitted to Probability Theory and Related Topics, 2007
Govind Menon
Mathematical approaches to dynamic scaling
J. Non-Newtonian Fluid Mech., 2007, doi:10.1016/j.jnnfm.2007.01.003
Govind Menon and R. Pego
Universality classes in Burgers turbulence
Comm. Math. Phys., 2007, doi:10.1007/s00220-007-0251-1
Govind Menon and R. Pego
The scaling attractor and ultimate dynamics for Smoluchowski’s coagulation equations
J. Nonlinear Sci., 2007.