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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/956| BLOWUP AND LIFE SPAN BOUNDS FOR A REACTION-DIFFUSION EQUATION WITH A TIME-DEPENDENT GENERATOR | |
| EKATERINA TODOROVA KOLKOVSKA | |
| Acceso Abierto | |
| Atribución-NoComercial-CompartirIgual | |
| Análisis Estocástico | |
| 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. | |
| Department of Mathematics Texas State University | |
| 2008 | |
| Artículo | |
| Inglés | |
| Investigadores | |
| PROCESOS ESTOCÁSTICOS | |
| Versión publicada | |
| publishedVersion - Versión publicada | |
| Appears in Collections: | Probababilidad Y Estadística |
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