Dynamical Systems and Probabilistic Methods in Partial Differential Equations

by Deift, Percy; Levermore, David C.; Wayne, Eugenec

• ISBN13: 9780821803684
• ISBN10: 0821803689
• Format: Paperback
• Copyright: 1995-11-01
• Publisher: Amer Mathematical Society
• More Book Details

Summary

The volumes in the Lectures in Applied Mathematics series contain lectures given at summer seminars in applied mathematics sponsored by the American Mathematical Society and the Society for Industrial and Applied Mathematics on various topics in applied mathematics. Among the themes explored in this volume are the following: * the increasing role of dynamical systems theory in understanding partial differential equations * the central importance of certain prototypical equations, such as the complex Ginzburg-Landau, nonlinear Schrödinger, and Korteweg-de Vries equations * problems in fluid mechanics and the limits of physically motivated heuristic theories of fluids.

Table of Contents

Dynamical Systems and PDEs: An introduction to KAM theory

KAM theory in infinite dimensions

Global center manifolds and singularly perturbed equations: A brief (and biased) guide to (some of) the literature

Melnikov analysis for PDE's

Exactly Integrable Systems: Integrable Hamiltonian systems

Amplitude Equations: The complex Ginzburg-Landau equation as a model problem

Derivation and justification of the complex Ginzburg-Landau equation as a modulation equation

Fluid Mechanics and Turbulence: Navier-Stokes equations and incompressible fluid turbulence

Turbulence as a near-equilibrium process

Homogenization and renormalization: The mathematics of multi-scale random media and turbulent diffusion

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