Non-Standard and Improperly Posed Problems

Karen A. Ames and Brian Straughan (Eds.)0-12-056745-8, 9780120567454

Written by two international experts in the field, this book is the first unified survey of the advances made in the last 15 years on key non-standard and improperly posed problems for partial differential equations.This reference for mathematicians, scientists, and engineers provides an overview of the methodology typically used to study improperly posed problems. It focuses on structural stability-the continuous dependence of solutions on the initial conditions and the modeling equations-and on problems for which data are only prescribed on part of the boundary.The book addresses continuous dependence on initial-time and spatial geometry and on modeling backward and forward in time. It covers non-standard or non-characteristic problems, such as the sideways problem for a heat or hyberbolic equation and the Cauchy problem for the Laplace equation and other elliptic equations. The text also presents other relevant improperly posed problems, including the uniqueness and continuous dependence for singular equations, the spatial decay in improperly posed parabolicproblems, the uniqueness for the backward in time Navier-Stokes equations on an unbounded domain, the improperly posed problems for dusty gases, the linear thermoelasticity, and the overcoming Holder continuity and image restoration.

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Table of contents :
Content:
Preface
Pages viii-ix
K.A. Ames, B. Straughan

1 Introduction Original Research Article
Pages 1-33

2 Continuous dependence on the geometry Original Research Article
Pages 34-102

3 Continuous dependence on modeling backward in time Original Research Article
Pages 103-182

4 Continuous dependence on modeling forward in time Original Research Article
Pages 183-216

5 Non-Standard and Non-Characteristic problems Original Research Article
Pages 217-237

6 Some further improperly posed problems Original Research Article
Pages 238-283

Bibliography
Pages 284-300

Index
Pages 301-303