BLOWUP AND LIFE SPAN BOUNDS FOR A REACTION-DIFFUSION EQUATION WITH A TIME-DEPENDENT GENERATOR
We consider the nonlinear equation @ @t u(t) = k(t)u(t) + u1+(t), u(0, x) = '(x), x 2 Rd, where := −(−)/2 denotes the fractional power of the Laplacian; 0 < 2, , > 0 are constants; ' is bounded, continuous, nonnegative function that does not vanish identically; and k is a locally int...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2008 |
| País: | México |
| Institución: | Centro de Investigación en Matemáticas |
| Repositorio: | Repositorio Institucional CIMAT |
| Idioma: | inglés |
| OAI Identifier: | oai:cimat.repositorioinstitucional.mx:1008/956 |
| Acceso en línea: | http://cimat.repositorioinstitucional.mx/jspui/handle/1008/956 |
| Access Level: | acceso abierto |
| Palabra clave: | info:eu-repo/classification/MSC/Análisis Estocástico 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 the nonlinear equation @ @t u(t) = k(t)u(t) + u1+(t), u(0, x) = '(x), x 2 Rd, where := −(−)/2 denotes the fractional power of the Laplacian; 0 < 2, , > 0 are constants; ' is bounded, continuous, nonnegative function that does not vanish identically; and k is a locally integrable function. We prove that any combination of positive parameters d, , , , obeying 0 < d/ < 1, yields finite time blow up of any nontrivial positive solution. Also we obtain upper and lower bounds for the life span of the solution, and show that the life span satisfies T' −/(−d) near = 0. |
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