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 recurso: | informe técnico |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| País: | México |
| Institución: | Centro de Investigación en Matemáticas |
| Repositorio: | Repositorio Institucional CIMAT |
| Idioma: | inglés |
| OAI Identifier: | oai:cimat.repositorioinstitucional.mx:1008/586 |
| Acceso en línea: | http://cimat.repositorioinstitucional.mx/jspui/handle/1008/586 |
| Access Level: | acceso abierto |
| Palabra clave: | 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 |
| Sumario: | 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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