Gui-Qiang Chen

Elton P. Hsu

Mark A. Pinsky

This book is a collection of original research papers and expository articles from the scientific program of the 2004-05 Emphasis Year on Stochastic Analysis and Partial Differential Equations at Northwestern University. Many well-known mathematicians attended the events and submitted their contributions for this volume. Topics from stochastic analysis discussed in this volume include stochastic analysis of turbulence, Markov processes, microscopic lattice dynamics, microscopic interacting particle systems, and stochastic analysis on manifolds. Topics from partial differential equations include kinetic equations, hyperbolic conservation laws, Navier-Stokes equations, and Hamilton-Jacobi equations. A variety of methods, such as numerical analysis, homogenization, measure-theoretical analysis, entropy analysis, weak convergence analysis, Fourier analysis, and Ito's calculus, are further developed and applied. All these topics are naturally interrelated and represent a cross-section of the most significant recent advances and current trends and directions in stochastic analysis and partial differential equations. This volume is suitable for researchers and graduate students interested in stochastic analysis, partial differential equations, and related analysis and applications.

Emphasis Year 2004-2005 on Stochastic Analysis and Partial Differential Equations, Northwestern University, Evanston, Illinois

Stochastic Analysis and Partial Differential Equations

Yanyan Li

Xiping Zhu

Daomin Chao

This volume is a collection of research papers on nonlinear partial differential equations and related areas, representing many aspects of the most recent developments in these important areas. In particular, the following are included: nonlinear conservation laws, semilinear elliptic equations, nonlinear hyperbolic equations, nonlinear parabolic equations, singular limit problems, and analysis of exact and numerical solutions. Important areas such as numerical analysis, relaxation theory, multiphase theory, kinetic theory, combustion theory, dynamical systems, and quantum field theory are also covered. Contents:Relaxation Limits for a Class of Balance Laws with Kinetic Formulation (Y Brenier et al.)Large-Time Behavior of Entropy Solutions in L∞ for Multidimensional Conservation Laws (G-Q Chen & H Frid)Indefinite Elliptic Problems with Critical Exponents (W-X Chen & C-B Li)Nonlinear Diffusive–Dispersive Limits for Multidimensional Conservation Laws (J-Q M C Correia & P G LeFloch)Two-Pressure Two Phase Flow (J Glimm et al.)Plainlevé Analysis and Its Applications (B-Y Guo & Z-X Chen)Stability of Traveling Wave Solutions for a Rate-Type Viscoelastic System (L Hsiao & T Luo)Generalized Rankine–Hugoniot Relations of Delta-Shocks in Solutions of Transportation Equations (J-Q Li & T Zhang)Geometric Measure of Nodals and Growth of Solutions to Elliptic Equations (F H Lin)A Note on Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations (L-W Lin)Strange Attractors in Pseudospectral Solutions of the Dissipative Zakharov Equations (S-Q Ma et al.)On Half-Space Problems for the Heat Equations with Nonlinear Boundary Conditions (M-X Wang & S Wang)String-Like Defects and Fractional Total Curvature in a Gauged Harmonic Map Model (Y-S Yang)Systems of Conservation Laws with Incomplete Sets of Eigenvectors Everywhere (Y-X Zhang)and other papers Readership: Mathematicians. Keywords:Nonlinear Partial Differential Equations;Proceedings;Conference;Beijing (China);Dedication

A Volume in Honor of Professor Xiaqi Ding

Advances in Nonlinear Partial Differential Equations and Related Areas

Hao Wang

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