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...

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Detalhes bibliográficos
Autores: Ferreira, R., de Pablo, A., Rossi, J.D.
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
Descrição
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.