The one-dimensional heat equation

書誌事項

The one-dimensional heat equation

John Rozier Cannon ; foreword by Felix E. Browder

(Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 23 . Section, Analysis)

Cambridge University Press, 2008, c1984

  • : pbk

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注記

Digitally printed version of original 1984 ed

Includes bibliographical references and indexes

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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詳細情報

  • NII書誌ID(NCID)
    BA9115132X
  • ISBN
    • 9780521089449
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Cambridge
  • ページ数/冊数
    xxv, 483 p.
  • 大きさ
    24 cm
  • 分類
  • 件名
  • 親書誌ID
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