**Contemporary Mathematics**

Volume: 429;
2007;
278 pp;
Softcover

MSC: Primary 35; 60; 82; 76; 58; 65;

Print ISBN: 978-0-8218-4059-7

Product Code: CONM/429

List Price: $86.00

Individual Member Price: $68.80

**Electronic ISBN: 978-0-8218-8108-8
Product Code: CONM/429.E**

List Price: $86.00

Individual Member Price: $68.80

# Stochastic Analysis and Partial Differential Equations

Share this page *Edited by *
*Gui-Qiang Chen; Elton Hsu; Mark 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 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.

#### Table of Contents

# Table of Contents

## Stochastic Analysis and Partial Differential Equations

- Table of Contents v6 free
- Preface vii8 free
- Construction of Suitable Weak Solutions of the Navier-Stokes Equations 110 free
- Error Estimates for Finite Difference-Quadrature Schemes for a Class of Nonlocal Bellman Equations with Variable Diffusion 1928
- Recent Progress in the Stochastic Analysis of Turbulent Mixing 3342
- Modified Keller-Segel System and Critical Mass for the Log Interaction Kernel 4554
- Entropy Solutions to Conservation Laws with Discontinuous Fluxes via Microscopic Interacting Particle Systems 6372
- Spectral Properties of Subordinate Processes in Domains 7786
- Smoluchowski Navier-Stokes Systems 8594
- Recent Developments in Stochastic Differential Equations 111120
- Heat Equations on Manifolds and Bismut's Formula 121130
- On a Class of One-dimensional Markov Processes with Continuous Paths 131140
- Prototype Hybrid Couplings of Macroscopic Deterministic Models and Microscopic Stochastic Lattice Dynamics 143152
- General Relative Entropy in a Nonlinear McKendrick Model 205214
- Pointwise Fourier Inversion in Analysis and Geometry 233242
- Stochastic Analysis and the KdV Equation 245254
- On Binary Fluid Mixtures 257266

#### Readership

Graduate students and research mathematicians interested in stochastic analysis and partical differential equations.