Global and Nonglobal Solutions of a System of Nonautonomous Semilinear Equations with Ultracontractive Lévy Generators
We consider a semilinear system of the form @ui(t; x)=@t = k(t)Aui(t; x) + ui i0 (t; x), with Dirichlet boundary conditions on a bounded open set D Rd, where k : [0;1) ! [0;1) is continuous, A is the initesimal generator of a symmetric Levy process Z fZ(t)gt0, i > 1, i 2 f1; 2g and i0 = 3 i. We g...
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| Tipo de documento: | relatório científico |
| Estado: | Versão publicada |
| Data de publicação: | 2014 |
| País: | México |
| Recursos: | Centro de Investigación en Matemáticas |
| Repositório: | Repositorio Institucional CIMAT |
| Idioma: | inglês |
| OAI Identifier: | oai:cimat.repositorioinstitucional.mx:1008/586 |
| Acesso em linha: | http://cimat.repositorioinstitucional.mx/jspui/handle/1008/586 |
| Access Level: | Acceso aberto |
| Palavra-chave: | info:eu-repo/classification/MSC/Procesos de Levy info:eu-repo/classification/cti/1 info:eu-repo/classification/cti/12 info:eu-repo/classification/cti/1208 info:eu-repo/classification/cti/120808 |
| Resumo: | We consider a semilinear system of the form @ui(t; x)=@t = k(t)Aui(t; x) + ui i0 (t; x), with Dirichlet boundary conditions on a bounded open set D Rd, where k : [0;1) ! [0;1) is continuous, A is the initesimal generator of a symmetric Levy process Z fZ(t)gt0, i > 1, i 2 f1; 2g and i0 = 3 i. We give conditions on D and on the Levy measure of Z under which our system possesses global positive solutions, or exhibits blow up in fnite time. Our approach is based on the intrinsic ultracontractivity property of the semigroup generated by the process Z killed on leaving D. |
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