The One-Dimensional Heat Equation

This is a version of Gevrey's classical treatise on the heat equations. Included in this volume are discussions of initial and/or boundary value problems, numerical methods, free boundary problems and parameter determination problems. The material is presented as a monograph and/or information source book. After the first six chapters of standard classical material, each chapter is written as a self-contained unit except for an occasional reference to elementary definitions, theorems and lemmas in previous chapters.

Editor's statement
Foreword
Preface
Preliminaries
Introduction
The Cauchy problem
The initial-value problem
The initial-boundary-value problem for the quarter plane with temperature-boundary specification
The initial-boundary-value problem for the quarter plane with heat-flux-boundary specification
The initial-boundary-value problem for the semi-infinite strip with temperature-boundary specification and heat-flux-boundary specification
The reduction of some initial-boundary-value problems for the semi-infinite strip, to integral equations: some exercises
Integral equations
Solutions of boundary-value problems for all times and periodic solutions
Analyticity of solutions
Continuous dependence upon the data for some state-estimation problems
Some numerical methods for some state-estimation problems
Determination of an unknown time-dependent diffusivity a(t) from overspecified data
Initial- and/or boundary-value problems for gneral regions with H÷lder continuous boundaries
Some properties of solutions in general domains
The solution in a general region with temperature-boundary specification: the method of perron-poincarF
The one-phase stefan problem with temperature-boundary specification
The one-phase stefan problem with flux-boundary specification: some exercises
The inhomogeneous heat equation ut=uxx+f(x,t)
An application of the inhomogeneous heat equation: the equation ut=uxx+f(x,t,u,ux)
Symbol index
Subject index
Table of Contents provided by Publisher. All Rights Reserved.

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The One-Dimensional Heat Equation

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Table of Contents

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