The role of non-linear diffusion in non-simultaneous blow-up
We study a parabolic system of two non-linear reaction-diffusion equations completely coupled through source terms and with power-like diffusivity. Under adequate hypotheses on the initial data, we prove that non-simultaneous blow-up is sometimes possible; i.e., one of the components blows up while...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2005 |
| País: | Argentina |
| Institución: | Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
| Repositorio: | Biblioteca Digital (UBA-FCEN) |
| Idioma: | inglés |
| OAI Identifier: | paperaa:paper_0022247X_v308_n1_p92_Brandle |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0022247X_v308_n1_p92_Brandle |
| Access Level: | acceso abierto |
| Palabra clave: | Blow-up Non-linear diffusion Parabolic system |
| Sumario: | We study a parabolic system of two non-linear reaction-diffusion equations completely coupled through source terms and with power-like diffusivity. Under adequate hypotheses on the initial data, we prove that non-simultaneous blow-up is sometimes possible; i.e., one of the components blows up while the other remains bounded. The conditions for non-simultaneous blow-up rely strongly on the diffusivity parameters and significant differences appear between the fast-diffusion and the porous medium case. Surprisingly, flat (homogeneous in space) solutions are not always a good guide to determine whether non-simultaneous blow-up is possible. © 2004 Elsevier Inc. All rights reserved. |
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