The One-Dimensional Heat Equation

John Rozier Cannon; Felix E. Browder

doi:10.1017/CBO9781139086967

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John Rozier Cannon, University of Central Florida
Foreword by Felix E. Browder

Publisher:: Cambridge University Press
Online publication date:: February 2012
Print publication year:: 1984
Online ISBN:: 9781139086967
DOI:: https://doi.org/10.1017/CBO9781139086967

Subjects:: Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory
Series:: Encyclopedia of Mathematics and its Applications (23)

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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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The One-Dimensional Heat Equation

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Contents

Frontmatter
pp i-x

Contents
pp xi-xviii

Editor's Statement
pp xix-xx

Foreword by Felix E. Browder
pp xxi-xxii

Preface
pp xxiii-xxvi

Chapter 0 - Preliminaries
pp 1-12

Chapter 1 - Introduction
pp 13-24

Chapter 2 - The Cauchy Problem
pp 25-31

Chapter 3 - The Initial-Value Problem
pp 32-44

Chapter 4 - The Initial-Boundary-Value Problem for the Quarter Plane with Temperature-Boundary Specification
pp 45-53

Chapter 5 - The Initial-Boundary-Value Problem for the Quarter Plane with Heat-Flux-Boundary Specification
pp 54-57

Chapter 6 - The Initial-Boundary-Value Problem for the Semi-Infinite Strip with Temperature-Boundary Specification and Heat-Flux-Boundary Specification
pp 58-66

Chapter 7 - The Reduction of Some Initial-Boundary-Value Problems for the Semi-Infinite Strip, to Integral Equations: Some Exercises
pp 67-81

Chapter 8 - Integral Equations
pp 82-100

Chapter 9 - Solutions of Boundary-Value Problems for All Times and Periodic Solutions
pp 101-110

Chapter 10 - Analyticity of Solutions
pp 111-127

Chapter 11 - Continuous Dependence upon the Data for Some State-Estimation Problems
pp 128-151

Chapter 12 - Some Numerical Methods for Some State-Estimation Problems
pp 152-186

Chapter 13 - Determination of an Unknown Time-Dependent Diffusivity a(t) from Overspecified Data
pp 187-212

Chapter 14 - Initial- and/or Boundary-Value Problems for General Regions with Hölder Continuous Boundaries
pp 213-251

Chapter 15 - Some Properties of Solutions in General Domains
pp 252-264

Chapter 16 - The Solution in a General Region with Temperature-Boundary Specification: The Method of Perron-Poincaré
pp 265-280

Chapter 17 - The One-Phase Stefan Problem with Temperature-Boundary Specification
pp 281-312

Chapter 18 - The One-Phase Stefan Problem with Flux-Boundary Specification: Some Exercises
pp 313-326

Chapter 19 - The Inhomogeneous Heat Equation ut = uxx + f(x, t)
pp 327-343

Chapter 20 - An Application of the Inhomogeneous Heat Equation: The Equation ut = uxx + F(x,t,u,ux)
pp 344-356

Some References to the Literature on ℒ(u) ≡ uxx – ut
pp 357-477

Symbol Index
pp 478-480

Subject Index
pp 481-483

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The One-Dimensional Heat Equation

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