The One-Dimensional Heat Equation

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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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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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