Stochastic Analysis and Partial Differential Equations
About this Volume
Edited by: Gui-Qiang Chen, Elton Hsu and Mark Pinsky
2007: Volume: 429
ISBNs: 978-0-8218-4059-7 (print); 978-0-8218-8108-8 (online)
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 Itô'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.
Graduate students and research mathematicians interested in stochastic analysis and partical differential equations.
Table of Contents
- Andrei Biryuk, Walter Craig and Slim Ibrahim – Construction of suitable weak solutions of the Navier-Stokes equations
- Imran H. Biswas, Espen R. Jakobsen and Kenneth H. Karlsen – Error estimates for finite difference-quadrature schemes for a class of nonlocal Bellman equations with variable diffusion
- Wurigen Bo, Baolian Cheng, Jian Du, Brian Fix, Erwin George, James Glimm, John W. Grove, Xicheng Jia, Hyeonseong Jin, Hyunsun Lee, Yuanhua Li, Xiaolin Li, Xinfeng Liu, David H. Sharp, Lingling Wu and Yan Yu – Recent progress in the stochastic analysis of turbulent mixing
- Vincent Calvez, Benoît Perthame and Mohsen Sharifi tabar – Modified Keller-Segel system and critical mass for the log interaction kernel
- Gui-Qiang Chen, Nadine Even and Christian Klingenberg – Entropy solutions to conservation laws with discontinuous fluxes via microscopic interacting particle systems
- Zhen-Qing Chen and Renming Song – Spectral properties of subordinate processes in domains
- Peter Constantin – Smoluchowski Navier-Stokes systems
- Shizan Fang – Recent developments in stochastic differential equations
- Elton P. Hsu – Heat equations on manifolds and Bismut’s formula
- Nobuyuki Ikeda and Yukio Ogura – On a class of one-dimensional Markov processes with continuous paths
- M. A. Katsoulakis, A. J. Majda and A. Sopasakis – Prototype hybrid couplings of macroscopic deterministic models and microscopic stochastic lattice dynamics
- Elena Kosygina – Homogenization of stochastic Hamilton-Jacobi equations: brief review of methods and applications
- P. Michel – General relative entropy in a nonlinear McKendrick model
- Mark A. Pinsky – Pointwise Fourier inversion in analysis and geometry
- Setsuo Taniguchi – Stochastic analysis and the KdV equation
- Konstantina Trivisa – On binary fluid mixtures