Stochastic Analysis and Partial Differential Equations (Contemporary Mathematics)

Stochastic Analysis and Partial Differential Equations (Contemporary Mathematics)

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Description

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.

Contents

Construction of suitable weak solutions of the Navier-Stokes equations by A. Biryuk, W. Craig, and S. Ibrahim Error estimates for finite difference-quadrature schemes for a class of nonlocal Bellman equations with variable diffusion by I. H. Biswas, E. R. Jakobsen, and K. H. Karlsen Recent progress in the stochastic analysis of turbulent mixing by W. Bo, B. Cheng, J. Du, B. Fix, E. George, J. Glimm, J. W. Grove, X. Jia, H. Jin, H. Lee, Y. Li, X. Li, X. Liu, D. H. Sharp, L. Wu, and Y. Yu Modified Keller-Segel system and critical mass for the log interaction kernel by V. Calvez, B. Perthame, and M. S. tabar Entropy solutions to conservation laws with discontinuous fluxes via microscopic interacting particle systems by G.-Q. Chen, N. Even, and C. Klingenberg Spectral properties of subordinate processes in domains by Z.-Q. Chen and R. Song Smoluchowski Navier-Stokes systems by P. Constantin Recent developments in stochastic differential equations by S. Fang Heat equations on manifolds and Bismut's formula by E. P. Hsu On a class of one-dimensional Markov processes with continuous paths by N. Ikeda and Y. Ogura Prototype hybrid couplings of macroscopic deterministic models and microscopic stochastic lattice dynamics by M. A. Katsoulakis, A. J. Majda, and A. Sopasakis Homogenization of stochastic Hamilton-Jacobi equations: Brief review of methods and applications by E. Kosygina General relative entropy in a nonlinear McKendrick model by P. Michel Pointwise Fourier inversion in analysis and geometry by M. A. Pinsky Stochastic analysis and the KdV equation by S. Taniguchi On binary fluid mixtures by K. Trivisa.

Product Details

  • ISBN13: 9780821840597
  • Format: Paperback
  • ID: 9780821840597
  • ISBN10: 0821840592

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