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:
-
Nabongo, Diabate
Boni, Théodore
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2007
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- 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/
- Palabra clave:
- Semidiscretizations
localized semilinear parabolic equation
semidiscrete quenching time
convergence.
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | 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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