Blow-up with logarithmic nonlinearities
We study the asymptotic behaviour of nonnegative solutions of the nonlinear diffusion equation in the half-line with a nonlinear boundary condition,{Mathematical expression} with p, q, λ > 0. We describe in terms of p, q and λ when the solution is global in time and when it blows up in finite tim...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2007 |
| País: | Argentina |
| Recursos: | Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
| Repositorio: | Biblioteca Digital (UBA-FCEN) |
| Idioma: | inglés |
| OAI Identifier: | paperaa:paper_00220396_v240_n1_p196_Ferreira |
| Acesso em linha: | http://hdl.handle.net/20.500.12110/paper_00220396_v240_n1_p196_Ferreira |
| Access Level: | acceso abierto |
| Palavra-chave: | Asymptotic behaviour Blow-up Nonlinear boundary conditions |
| Resumo: | We study the asymptotic behaviour of nonnegative solutions of the nonlinear diffusion equation in the half-line with a nonlinear boundary condition,{Mathematical expression} with p, q, λ > 0. We describe in terms of p, q and λ when the solution is global in time and when it blows up in finite time. For blow-up solutions we find the blow-up rate and the blow-up set and we describe the asymptotic behaviour close to the blow-up time, showing that a phenomenon of asymptotic simplification takes place. We finally study the appearance of extinction in finite time. © 2007 Elsevier Inc. All rights reserved. |
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