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Lefschetz Center for Dynamical Systems

Publications

 


2013

Harold Kushner
A partial history of the early development of continuous-time nonlinear stochastic systems theory
PDF


2012

Constantine Dafermos
Maximal dissipation in equations of evolution
J. Diff. Equations 252 (2012), 567-587
PDF

Constantine Dafermos
N-waves in hyperbolic balance laws
Journal of Hyperbolic Equations, (to appear)

Constantine Dafermos
Hyperbolic Conservation Laws: Analytical Properties
Encyclopedia of Applied and Computational Mathematics
. B. Engquist (ed.) Springer-Verlag, Berlin (to appear)

Constantine Dafermos
Regularity of solutions to the equations of thermoelasticity
Encyclopedia of Thermal Stresses. R. Hetnarski (ed.) Springer-Verlag, Berlin (to appear)

Hongjie Dong
Solvability of second-order equations with hierarchically partially BMO coefficients
Trans. Amer. Math. Soc., 364 (2012) no. 1, 493–517

PDF

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
PDF

Paul Dupuis and Y. Cai
Analysis of an interacting particle method for rare event estimation
submitted

Paul Dupuis, Y. Liu, N. Plattner and J. D. Doll
On the infinite swapping limit for parallel tempering
submitted
PDF

Paul Dupuis, K. Spiliopoulos and H. Wang
Importance sampling for multiscale diffusions
to appear in SIAM J. on Multiscale Modeling and Simulation
PDF

Paul Dupuis, B. Kaynar, A. Ridder, R. Rubinstein and Radislav Vaisman
Counting with combined splitting and capture-recapture methods
submitted
PDF

Paul Dupuis and K. Chowdhary
Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification
to appear in ESAIM: Mathematical Modelling and Numerical Analysis
PDF

Paul Dupuis and K. Spiliopoulos
Large deviations for multiscale diffusions via weak convergence methods
to appear in Stochastic Processes and Their Applications
PDF

Paul Dupuis and M. Fischer
On the construction of Lyapunov functions for nonlinear Markov processes via relative entropy
submitted
PDF

Paul Dupuis, A. Budhiraja and M. Fischer
Large deviation properties of weakly interacting processes via weak convergence methods
to appear in Annals of Probability
PDF

Justin Holmer (with Quanhui Lin) 
Phase-driven interaction of widely separated nonlinear Schroedinger solitons
to appear in Journal of Hyperbolic Differential Equations
PDF

Justin Holmer (with Svetlana Roudenko) 
Blow-up solutions on a sphere for the 3d quintic NLS in the energy space
to appear in Analysis and PDE
PDF

Justin Holmer
Dynamics of KdV solitons in the presence of a slowly varying potential
to appear in IMRN Internat. Math. Res. Notices
PDF

Harold Kushner
Modeling and Approximations for Stochastic Systems with State-Dependent Singular Controls and Wide-Band Noise
accepted for 2012 IEEE CDC Conference on Decision and Control
PDF

Harold Kushner
Controlled Nonlinear Stochastic Delay Equations:  Part I: Modeling and Approximations
Applied Math and Optimization, Vol. 66, 2012, pages 77-54
PDF

 

Harold Kushner
Controlled Nonlinear Stochastic Delay Equations: Part II: Appxoximations and Pipe-Flow Representations
Applied Math and Optimization, Vol. 66, 2012, pages 55-80
PDF

B Sandstede, A Scheel, G Schneider and H Uecker
Diffusive mixing of periodic wave trains in reaction-diffusion systems
Journal of Differential Equations (2012), (accepted)
PDF

P van Heijster and B Sandstede
Coexistence of stable spots and fronts in a three-component Fitzhugh-Nagumo system
RIMS Kokyuroku Bessatsu (2012), (accepted)
PDF

HJ Hupkes and B Sandstede
Stability of pulse solutions for the discrete FitzHugh-Nagumo system
Transactions of the American Mathematical Society (2012), (accepted)
PDF

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
DOI

 


2011

Constantine Dafermos
Generalized characteristics and the Hunter-Saxton equation
Journal of Hyperbolic Equations,
8 (2011), 159-168
PDF

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
PDF

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
PDF

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
PDF

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., to appear (2011)
PDF

Hongjie Dong
On similarity solutions to the multidimensional aggregation equation
SIAM J. Math.Anal.
, 43 (2011) no. 4, 1995–2008
PDF

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
PDF

Hongjie Dong and D. Kim
On Lp-estimates for a class of nonlocal elliptic equations
J. Funct. Anal., to appear (2011), doi:10.1016/j.jfa.2011.11.002
PDF

Hongjie Dong
Parabolic equations with variably partially VMO coefficients
Algebra i Analis (St. Petersburg Math. J.) 23 (2011) no.3, 150–174
PDF

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
PDF

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
PDF

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
PDF

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
PDF

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
PDF

Paul Dupuis, A. Budhiraja and V. Maroulas

Variational representations for continuous time processes
Annales de l.Institut Henri Poincaré, 47, (2011), 725-747
PDF

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
PDF

Yan Guo and I. Tice
Rayleigh-Taylor instability for compressible inviscid fluids
Indiana University  Math., in press (2011)
PDF

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
PDF

Yan Guo and B. Pausader
Global smooth ion dynamics in the Euler-Poisson system
Commun. Math. Phys. 303 (2011), no. 1, 89-125
PDF

Yan Guo and T. Nguyen
A note on Prandtl layer problem
Comm. Pure Appl. Math., 64, (2011) no. 10, 1416-1438
PDF

Yan Guo and R. Strain
Momentum regularity and stability of the relativistic Vlasov-Maxwell-Boltzmann system

accepted in Commun. Math. Phys. (2011)
PDF

Yan Guo
The Vlasov-Poisson-Landau system in a periodic box
Journal of AMS (2011)
PDF

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 
PDF 

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
PDF

HJ Hupkes, D Pelinovsky and B Sandstede
Propagation failure in the discrete Nagumo equation
Proceedings of the American Mathematical Society 139 (2011) 3537-3551
PDF


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
PDF

Harold Kushner
Controlled Nonlinear Stochastic Delay Equations: Part II: Approximations and Pipe-Flow Representations
PDF

Harold Kushner
Numerical Methods for Stochastic Singular Control Problems with State-Dependent Control
to appear SIAM J on Control and Optimization
PDF

Harold Kushner
Numerical Methods for Controls for Nonlinear Stochastic Systems With Delays and   Jumps:  Applications to Admission Control
Stochastics: An International Journal of Probabiity and Statistics, Vol. 83, 20111, pages 277-310
(PDF)

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
PDF

John Mallet-Paret and R. D. Nussbaum
Inequivalent measures of noncompactness
Annali di Matematica 190 (2011), pp. 453–488
PDF

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
PDF

Weining Kang and Kavita Ramanan
Characterization of Stationary Distributions of Reflected Diffusions

PDF

P van Heijster and B Sandstede 
Planar radial spots in a three-component FitzHugh-Nagumo system
Journal of Nonlinear Science 21 (2011) 705-745
PDF

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
PDF

Hui Wang, P. Dupuis and K. Spiliopoulos
Rare event simulation for rough energy landscapes
Proceeding of the 2011 Winter Simulation Conference, 2011
PDF

Hui Wang and L. Setayeshgar
Large deviations for a feedforward network
Adv. Appl. Prob. 43, 545-571, 2011



2010

W.H.Fleming, H. Kaise and S-J. Sheu,
Max-plus Stochastic Control and Risk Sensitivity
(PDF)

W.H. Fleming and D. Hernandez-Hernandez,
On the Value of Stochastic Differential Games
(PDF)

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
(PDF)


2009

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
(PDF)

Harold Kushner
Large Deviations  for Two-Time-Scale  Diffusions, With Delays
(PDF)


2008

Abdelkader Boucherif
Nonlocal Problems for Parabolic Inclusions
(PDF)

Abdelkader Boucherif, Zehour Benbouziane, and Sidi Mohamed Bouguima
Existence Result for Impulsive Third Order Periodic Boundary Value Problems
(PDF)

 Hongjie Dong and Dong Li
Optimal local smoothing and analyticity rate estimates for the generalized Navier-Stokes equations
 Comm. Math. Sci., to appear
 (PDF)

Hongjie Dong and Dong Li
Finite time singularities for a class of generalized surface quasi-geostropic equations
Proc. Amer. Math., 136 (2008), 2555--2563
(PDF)

Hongjie Dong and Seick Kim
Green's matrices of second order elliptic systems with measurable coefficients in two dimensional domains
Trans. Amer. Math. Soc., to appear
(PDF)


Hongjie Dong
Well-posedness for a transport equation with nonlocal velocity
J. Funct. Anal, to appear
(PDF)

Hongjie Dong and Doyoon Kim
Parabolic and elliptic systems with VMO coefficients
 (PDF)

Hongjie Dong and Natas Pavlovic
Regularity criteria for the dissipative quasi-geostrophic equations in Hölder spaces
Comm. Math. Phys., to appear
(PDF)

Hongjie Dong and Nicolai V. Krylov
Second-order elliptic and parabolic equations with B(R2, VMO) coefficients
Submitted.
(PDF)

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
(PDF)

Paul Dupuis and Thomas Dean
The design and analysis of a generalized DPR algorithm for rare event simulation
(PDF)

Yan Guo and Mahir Hadzic
Stability in the Stefan problem with surface tension (I)
(PDF)

Yan Guo and R. Strain
Decay for soft potentials near Maxwellian
Arch. Rational Mech. Anal., 187 no. 2, 287-339. (2008)
(PDF)

Yan Guo and H. Hwang
Pattern formation (I): The Keller-Segel model
JDE, accepted
(PDF)

Yan Guo and Z. Lin
Unstable and stable galaxy models
Commun. Math. Phys., accepted
(PDF)

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 (accepted)
(PDF)

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
PDF Hexagon 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
(PDF)

Bjorn Sandstede and A. Scheel
Hopf bifurcation from viscous shock waves
SIAM Journal on Mathematical Analysis 39 (2008) 2033-2052
(PDF)

B Sandstede and N. Kutz
Theory of passive harmonic mode-locking using waveguide arrays
Optics Express 16 (2008) 636-650
(PDF)

Bjorn Sandstede and A. Scheel
Relative Morse indices, Fredholm indices, and group velocities
Discrete and Continuous Dynamical Systems A 20 (2008) 139-158
(PDF)

Hui Wang and Paul Dupuis 
Importance Sampling for Jackson Networks
(PDF)

Hui Wang, Paul Dupuis and Kevin Leder
Importance Sampling for Weighted-Serve-the-Longest-Queue
(PDF)


2007

Hongjie Dong and Dapeng Du
Global well-posedness and a decay estimate for the critical quasi-geostrophic equation
To appear in Discrete Contin. Dyn. Syst., 2007
(PDF)

Hongjie Dong, Sungwon Cho and Seick Kim
On the fundamental solutions for strongly parabolic systems of second order
To appear in I.U.M.J., 2007
(PDF)

Hongjie Dong and N. Pavlovic
A regularity criterion for the dissipative quasi-geostrophic equations.
(PDF)

Amarjit Budhiraja, Paul Dupuis, and Vasileios Maroulasz
Large Deviations for Stochastic Flows of Diffeomorphisms.
(PDF)

Paul Dupuis, Kevin Leder, and HuiWang
Large deviations and importance sampling for a tandem network with slow-down
(PDF)

Paul Dupuis, Kevin Leder and Hui Wang
On the Large Deviations Properties of theWeighted-Serve-the-Longest-Queue Policy
Progress in Probability, accepted      
(PDF)

Thomas Dean, and Paul Dupuis
Splitting for Rare Event Simulation: A Large Deviations Approach to Design and Analysis
(PDF)

Amarjit Budhiraja, Paul Dupuis, and Vasileios Maroulas (March 2007)
Large Deviations for Infinite Dimensional Stochastic Dynamical Systems
(PDF)

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
(PDF)

Yan Guo, C. Hallstrom and D. Spirn
Dynamics near unstable, interfacial fluids
Commun. Math. Phys., 270 (2007), 635-689
(PDF)

Yan Guo and H. Hwang
Pattern formation (II): The Turing instability
Proc. AMS, 135 (2007), 2855-2866
(PDF)

Henrik Hult and Gennady Samorodnitsky
Tail probabilities for infinite series of regularly varying random vectors
(PDF)

Harold J. Kushner
Numerical Approximations to Optimal Nonlinear Filters
(PDF)

S. V. Lototsky and B. L. Rozovskii
Stochastic Partial Differential Equations Driven by Purely Spatial Noise
Submitted to SIAM Journal on Mathematical Analysis, 2007
(PDF)

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

 (PDF)

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
(PDF)

Govind Menon
Mathematical approaches to dynamic scaling.
J. Non-Newtonian Fluid Mech., 2007, doi:10.1016/j.jnnfm.2007.01.003
(PDF)

Govind Menon and R. Pego
Universality classes in Burgers turbulence.
 Comm. Math. Phys., 2007, doi:10.1007/s00220-007-0251-1
 (PDF)

Govind Menon and R. Pego
The scaling attractor and ultimate dynamics for Smoluchowski's coagulation equations.
J. Nonlinear Sci., 2007, to appear
(PDF)

 

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