Radial equivalence for the two basic nonlinear degenerate diffusion equations |
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| Authors: | Razvan Gabriel Iagar Ariel Sánchez Juan Luis Vázquez |
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| Affiliation: | 1. Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain;2. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-014700, Bucharest, Romania;3. Departamento de Matemática Aplicada, Universidad Rey Juan Carlos, Móstoles, 28933 Madrid, Spain |
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| Abstract: | In this paper we prove that there exists an explicit correspondence between the radially symmetric solutions of two well-known models of nonlinear diffusion, the porous medium equation and the p-Laplacian equation. We establish exact correspondence formulas between these solutions. We also study in detail the application of the results in the important case of self-similar solutions. In particular, we derive the existence of new self-similar solutions for the evolution p-Laplacian equation. |
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