Some results on blow up for semilinear parabolic problems
The authors describe the asymptotic behavior of blow-up for the semilinear heat equation ut=uxx+f(u) in R×(0,T), with initial data u0(x)>0 in R, where f(u)=up, p>1, or f(u)=eu. A complete description of the types of blow-up patterns and of the corresponding blow-up final-time profiles is given...
| Autores: | , |
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| Tipo de recurso: | capítulo de libro |
| Fecha de publicación: | 1993 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/60763 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/60763 |
| Access Level: | acceso abierto |
| Palabra clave: | 517.956.4 Semilinear parabolic problems blow up asymptotic behaviour of solutions Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias |
| Sumario: | The authors describe the asymptotic behavior of blow-up for the semilinear heat equation ut=uxx+f(u) in R×(0,T), with initial data u0(x)>0 in R, where f(u)=up, p>1, or f(u)=eu. A complete description of the types of blow-up patterns and of the corresponding blow-up final-time profiles is given. In the rescaled variables, both are governed by the structure of the Hermite polynomials H2m(y). The H2-behavior is shown to be stable and generic. The existence of H4-behavior is proved. A nontrivial blow-up pattern with a blow-up set of nonzero measure is constructed. Similar results for the absorption equation ut=uxx−up, 0<p<1, are discussed. |
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