Dynamical Systems and Probabilistic Methods in Partial Differential Equations: 1994 Summer Seminar on Dynamical Systems and Probabilistic Methods for

Dynamical Systems and Probabilistic Methods in Partial Differential Equations: 1994 Summer Seminar on Dynamical Systems and Probabilistic Methods for

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Description

This volume contains some of the lectures presented in June 1994 during the AMS-SIAM Summer Seminar at the Mathematical Sciences Research Institute in Berkeley. The goal of the seminar was to introduce participants to as many interesting and active applications of dynamical systems and probabilistic methods to problems in applied mathematics as possible. As a result, this book covers a great deal of ground. Nevertheless, the pedagogical orientation of the lectures has been retained, and therefore the book will serve as an ideal introduction to these varied and interesting topics.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 Schrodinger, and Korteweg-deVries equations problems in fluid mechanics and the limits of physically motivated heuristic theories of fluids the role of probabilistic methods in studying turbulent phenomena.

Contents

Section I: Dynamical Systems and PDEs: An introduction to KAM theory by C. E. Wayne KAM theory in infinite dimensions by W. Craig Global center manifolds and singularly perturbed equations: A brief (and biased) guide to (some of) the literature by N. Kopell Melnikov analysis for PDE's by D. W. McLaughlin and J. Shatah Section II: Exactly Integrable Systems: Integrable Hamiltonian systems by P. Deift Section III: Amplitude Equations: The complex Ginzburg-Landau equation as a model problem by C. D. Levermore and M. Oliver Derivation and justification of the complex Ginzburg-Landau equation as a modulation equation by A. Mielke and G. Schneider Section IV: Fluid Mechanics and Turbulence: Navier-Stokes equations and incompressible fluid turbulence by P. Constantin Turbulence as a near-equilibrium process by A. J. Chorin Homogenization and renormalization: The mathematics of multi-scale random media and turbulent diffusion by M. Avellaneda.

Product Details

  • ISBN13: 9780821803684
  • Format: Paperback
  • ID: 9780821803684
  • ISBN10: 0821803689

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