A weighted quasilinear equation related to the mean curvature operator |
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| Authors: | Santiago Cano-Casanova Julián López-Gómez Kazuhiro Takimoto |
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| Institution: | 1. Departamento de Matemática Aplicada y Computación, Universidad Pontificia Comillas, Alberto Aguilera 25, 28015-Madrid, Spain;2. Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040-Madrid, Spain;3. Department of Mathematics, Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima City, Hiroshima 739-8526, Japan |
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| Abstract: | This paper studies a weighted quasilinear perturbation, through the mean curvature flow operator, of the classical linear heat equation. The mean curvature has the effect of maintaining bounded all classical positive steady states of the model, though their derivatives must be somewhere unbounded. The dynamics of the positive solutions of the model is fully described. |
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| Keywords: | 35K59 35K93 |
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