A Free-Boundary Problem for a Degenerate Parabolic System.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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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
- Numerical Mathematics