Non-Standard and Improperly Posed Problems (ISSN Book 194)

Brian Straughan

William F. Ames

Academic Press

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.

Non-Standard and Improperly Posed Problems (Volume 194) (Mathematics in Science and Engineering, Volume 194)

Science & Math

K. A. Ames

Mathematics

This book is primarily a presentation of nonlinear energy stability obtained in convection problems by means of an integral inequality technique that is referred to as the energy method. While its use was originally based on the kinetic energy of the fluid motion, subsequent work has introduced variations of the classical energy. The new functionals have much in common with the Lyapunov method in partial differential equations and standard terminology in the literature would now appear to be generalized energy methods. In this book, the author describes many of the new generalizations and explains why such a generalization was deemed necessary. Additionally, he explains the physical relevance of the problem and indicates the usefulness of an energy technique in this context.

The Energy Method, Stability, and Nonlinear Convection (Applied Mathematical Sciences)

Physics

Springer, Verlag

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Books by Brian Straughan