The One-Dimensional Heat Equation
Part of Encyclopedia of Mathematics and its Applications
- Author: John Rozier Cannon, University of Central Florida
- Date Published: November 2008
- availability: Available
- format: Paperback
- isbn: 9780521089449
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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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- Date Published: November 2008
- format: Paperback
- isbn: 9780521089449
- length: 512 pages
- dimensions: 234 x 156 x 26 mm
- weight: 0.71kg
- availability: Available
Table of Contents
Editor's statement
Foreword Felix E. Browder
Preface
Preliminaries
1. Introduction
2. The Cauchy problem
3. The initial-value problem
4. The initial-boundary-value problem for the quarter plane with temperature-boundary specification
5. The initial-boundary-value problem for the quarter plane with heat-flux-boundary specification
6. The initial-boundary-value problem for the semi-infinite strip with temperature-boundary specification and heat-flux-boundary specification
7. The reduction of some initial-boundary-value problems for the semi-infinite strip, to integral equations: some exercises
8. Integral equations
9. Solutions of boundary-value problems for all times and periodic solutions
10. Analyticity of solutions
11. Continuous dependence upon the data for some state-estimation problems
12. Some numerical methods for some state-estimation problems
13. Determination of an unknown time-dependent diffusivity a(t) from overspecified data
14. Initial- and/or boundary-value problems for gneral regions with Hölder continuous boundaries
15. Some properties of solutions in general domains
16. The solution in a general region with temperature-boundary specification: the method of perron-poincaré
17. The one-phase stefan problem with temperature-boundary specification
18. The one-phase stefan problem with flux-boundary specification: some exercises
19. The inhomogeneous heat equation ut=uxx+f(x,t)
20. An application of the inhomogeneous heat equation: the equation ut=uxx+f(x,t,u,ux)
Symbol index
Subject index.
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