The one-dimensional heat equation
著者
書誌事項
The one-dimensional heat equation
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 23 . Section,
Cambridge University Press, 1984
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注記
Imprint and ISBN from label on t.p. verso. Imprint on t.p.: Reading Mass. : Addison-Wesley, Advanced Book Program, 1984
Publication taken over by Cambridge University Press in 1984
"Some references to the literature on £(u)=u[xx]-u[t]": p. 357-477
Includes index
[xx],[t]: subscript
内容説明・目次
内容説明
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.
目次
- 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 Hoelder 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.
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