We prove the existence of a one-parameter family of solutions of the porous medium equation, a nonlinear heat equation. In our work, with space dimension 3, the interface is a half line whose end point advances at constant speed. We prove, by using maximum principle, that the solutions are stable under a suitable class of perturbations. We discuss the relevance of our solutions, when restricted to two dimensions, to gravity driven flows of thin films. Here we extend the results of J. Iaia and S. Betelu in the paper "Solutions of the porous medium equation with degenerate interfaces" to a higher dimension.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc271876 |
| Date | 05 1900 |
| Creators | Paudel, Laxmi P. |
| Contributors | Iaia, Joseph, Liu, Jianguo, Allaart, Pieter C. |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | Text |
| Rights | Public, Paudel, Laxmi P., Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved. |
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