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The One-Dimensional Heat Equation

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The One-Dimensional Heat Equation

The One-Dimensional Heat Equation

John Rozier Cannon, University of Central Florida
Felix E. Browder
November 2008
Available
Paperback
9780521089449
    Description

    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.

    Product details

    November 2008
    Paperback
    9780521089449
    512 pages
    234 × 156 × 26 mm
    0.71kg
    Available

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    Contents

    Table of Contents

    • 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 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.
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    About the authors
      Contributors

    • Felix E. Browder

      • Author
    • John Rozier Cannon , University of Central Florida
    • Felix E. Browder

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