The One-Dimensional Heat Equation

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Cambridge University Press, Dec 28, 1984 - Mathematics - 483 pages
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.
 

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Contents

Preliminaries
1
Analy ticiry of Solutions
10
Introduction
13
The Cauchy Problem
25
The InitialValue Problem
32
The InitialBoundaryValue Problem for the Quarter
45
The InitialBoundaryValue Problem for the Quarter
54
The Reduction of Some InitialBoundaryValue
67
Determination of an Unknown TimeDependent
187
Initial andor BoundaryValue Problems
213
Some Properties of Solutions in General Domains
252
The Solution in a General Region with
265
The OnePhase Stefan Problem with
281
The OnePhase Stefan Problem with
313
The Inhomogeneous Heat Equation u wtr +
327
Some References to the Literature on JFu uII u
357

Integral Equations
82
Solutions of BoundaryValue Problems
101
Continuous Dependence upon the Data
128
Some Numerical Methods for Some StateEstimation
152
19501973
368
19731981
408
Symbol Index
478
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Page 451 - Target patterns and horseshoes from a perturbed central-force problem: some temporally periodic solutions to reaction-diffusion equations, Stud. Appl. Math. 64 (1981), No.
Page 395 - Free boundary problems for the heat equation in which the moving interface coincides initially with the fixed face.

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