On a general approach to extinction and blow-up for quasi-linear heat equations
The authors study asymptotic behaviour of positive solutions of equations of the type ut =Δφ(u)±Q(u), where φ′ and Q are given positive functions. By determining an auxiliary function F(u) appearing in an expression posed by A. Friedman and B. McLeod, they obtain asymptotic estimates of solutions as...
| Autores: | , , , |
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| Formato: | artículo |
| Fecha de publicación: | 1993 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/57858 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/57858 |
| Access Level: | acceso abierto |
| Palavra-chave: | 517.956.4 536.2 Friedman-McLeod method blow-up extinction point heat equation Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias |
| Resumo: | The authors study asymptotic behaviour of positive solutions of equations of the type ut =Δφ(u)±Q(u), where φ′ and Q are given positive functions. By determining an auxiliary function F(u) appearing in an expression posed by A. Friedman and B. McLeod, they obtain asymptotic estimates of solutions as t→T, blow-up or extinction time. These estimates have been established by other authors using different methods. Moreover, the paper poses a conjecture that, if the behaviour of u(0,t) as t→T near a blow-up or extinction point is known, all the information about the corresponding asymptotic expansions on small compact subsets near the origin is encoded in the first order ODE φ′(u)ur+rF(u)=0 for r>0 as t→T, where an optimal choice of F(u) is indicated in the paper. |
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