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The One-Dimensional Heat Equation

Part of Encyclopedia of Mathematics and its Applications

Felix E. Browder
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  • Date Published: November 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521089449


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About the Authors
  • 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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    Product details

    • Date Published: November 2008
    • format: Paperback
    • isbn: 9780521089449
    • length: 512 pages
    • dimensions: 234 x 156 x 26 mm
    • weight: 0.71kg
    • availability: Available
  • Table of Contents

    Editor's statement
    Foreword Felix E. Browder
    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.

  • Author

    John Rozier Cannon, University of Central Florida


    Felix E. Browder


    Felix E. Browder

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