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Intermediate Asymptotics for Inhomogeneous Nonlinear Heat Conduction |
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| Authors: | V A Galaktionov S Kamin R Kersner J L Vazquez |
| Institution: | 1. Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK 2. Keldysh Institute of Applied Mathematics, Miusskaya Sq. 4, 125047, Moscow, Russia 3. Raymond and Beverly Sackler Faculty of Exact Sciences, School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel 4. Computer and Automation Research Institute of the Hungarian Academy of Science, H-1518 Budapest, POB 63, Hungary 5. Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049, Madrid, Spain |
| Abstract: | We consider the initial-value problem for a quasilinear heat-conduction or diffusion equation with variable density decreasing at infinity. We show that the asymptotic behavior of the given process is self-similar. Indeed, as t   the solution of the problem approaches a self-similar solution of a certain singular  limit equation. The limit solution has compact support for any t > 0 and cusp-type shape at the space origin. |
| Keywords: | nonlinear parabolic equation variable coefficient self-similar solution asymptotic behavior |
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