Please use this identifier to cite or link to this item: 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
Appears in Collections:Reportes Técnicos - Probabilidad y Estadística

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