The One-Dimensional Heat Equation [Paperback]

This is a version of Gevrey's classical treatise on the heat equations.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.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.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 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 al