Numerical quenching solutions of localized semilinear parabolic equation
This paper concerns the study of the numerical approximationfor the following initial-boundary value problem:ut(x; t) = uxx(x; t) + E(1 - u(0; t))-p; (x; t) 2 (-l; l) x (0; T),u(-l; t) = 0; u(l; t) = 0; t in (0; T),u(x; 0) = u0(x) and gt;= 0; x in (-l; l),where p and gt; 1, l = 1/2 and E and gt; 0....
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2007 |
| País: | Colombia |
| Institución: | Universidad Nacional de Colombia |
| Repositorio: | Repositorio UN |
| Idioma: | español |
| OAI Identifier: | oai:repositorio.unal.edu.co:unal/73616 |
| Acceso en línea: | https://repositorio.unal.edu.co/handle/unal/73616 http://bdigital.unal.edu.co/38092/ |
| Access Level: | acceso abierto |
| Palabra clave: | Semidiscretizations localized semilinear parabolic equation semidiscrete quenching time convergence. |
| Sumario: | This paper concerns the study of the numerical approximationfor the following initial-boundary value problem:ut(x; t) = uxx(x; t) + E(1 - u(0; t))-p; (x; t) 2 (-l; l) x (0; T),u(-l; t) = 0; u(l; t) = 0; t in (0; T),u(x; 0) = u0(x) and gt;= 0; x in (-l; l),where p and gt; 1, l = 1/2 and E and gt; 0. Under some assumptions, we prove that the solution of a semidiscrete form of the above problem quenches in a nite time and estimate its semidiscrete quenching time. We also show that the semidiscrete quenching time in certain cases converges to the real one when the mesh size tends to zero. Finally,we give some numerical experiments to illustrate our analysis. |
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