A Free-Boundary Problem for a Degenerate Parabolic System.

Abstract

The degenerate parabolic system (1.1) in the introduction, serves as a model for heat conduction in a heterogeneous medium consisting of two components. The first component is made up of small pieces suspended in the second component, and the second component undergoes a change of phase at a prescribed temperature. This phenomenon occurs in a mixture of gravel and wet soil (for example, melting of frozen soil). Existence and uniqueness results of weak solutions of the degenerate parabolic problem are shown by employing monotone operator theory. Local regularity, such as continuity and boundedness of the solution is studied. A discussion is provided about the mutual interplay of the thermodynamic temperature (the temperature in the first component) and the conductive temperature (the temperature in the second component. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1981
Accession Number
ADA110469

Entities

People

  • R. E. Showalter

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Composite Materials
  • Continuity
  • Differential Equations
  • Equations
  • Formulas (Mathematics)
  • Functional Analysis
  • Heat Energy
  • Heat Of Fusion
  • Hilbert Space
  • Latent Heat
  • Liquid Phases
  • Mathematics
  • Partial Differential Equations
  • United States
  • Wisconsin

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Plasma Physics / Magnetohydrodynamics