The One-Dimensional Heat Equation

ISBN: 9780521089449 出版年：1984 页码：512 John Rozier Cannon Felix E Browder Cambridge University Press

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 Holder 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-poincare 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.