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...

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Detalles Bibliográficos
Autores: Brändle, C., Quirós, F., Rossi, J.D.
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
Descripción
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.