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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/664| Finite Time Blowup and Life Span of a Nonautonomous Semilinear Equation | |
| EKATERINA TODOROVA KOLKOVSKA | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| Análisis Estocático | |
| Consider the semilinear nonautonomous equation @ @t u ( t ) = k ( t )¢ Æ u ( t ) + u 1+ Ø ( t ) with u (0 ; x ) = ∏' ( x ), x 2 R d , where ¢ Æ := ° ( ° ¢) Æ= 2 ; 0 < Æ ∑ 2, ∏ , Ø > 0 are constants, ' ∏ 0 is bounded, continuous and does not identically vanish, and k : [0 ; 1 ) ! [0 ; 1 ) is a locally integrable function satisfying " 1 t Ω ∑ R t 0 k ( r ) dr ∑ " 2 t Ω for all t large enough, where " 1 ; " 2 ; Ω > 0 are given constants. We prove that any constellation of positive parameters d; Æ; Ω; Ø , obeying 0 < dΩØ=Æ < 1, yields Ønite time blow up of any nontrivial positive solution. Under suitable additional assumptions, we also obtain upper and lower bounds for the life span T ∏' of the above equation, which prove that T ∏' ª ∏ ° ÆØ Æ ° dΩØ near zero. | |
| Centro de Investigación en Matemáticas AC | |
| 14-12-2006 | |
| Reporte | |
| Inglés | |
| Investigadores | |
| PROCESOS ESTOCÁSTICOS | |
| Versión publicada | |
| publishedVersion - Versión publicada | |
| Aparece en las colecciones: | Reportes Técnicos - Probabilidad y Estadística |
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