Modelo semidiscreto para una ecuación de difusión no local con fuente
We study a discrete model for a non-local diffusion problem with a source, namely (ui) ′ (t) = Nj=−N hJ h(i − j) uj(t) – N j=−N hJ h(i − j) ui(t) + f(ui(t)), with initial datum ui(0) = u0(xi) > 0. We prove the existence and uniqueness of the solution. Moreover, we show that solutions of discre...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2012 |
| País: | Colombia |
| Recursos: | Universidad Industrial de Santander |
| Repositorio: | Repositorio UIS |
| Idioma: | español |
| OAI Identifier: | oai:noesis.uis.edu.co:20.500.14071/7335 |
| Acesso em linha: | https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/2900 https://noesis.uis.edu.co/handle/20.500.14071/7335 |
| Access Level: | acceso abierto |
| Palavra-chave: | nonlocal diffusion Neumann boundary conditions semidiscretization blow-up difusión no local condiciones de Neumann semidiscretización explosión |
| Resumo: | We study a discrete model for a non-local diffusion problem with a source, namely (ui) ′ (t) = Nj=−N hJ h(i − j) uj(t) – N j=−N hJ h(i − j) ui(t) + f(ui(t)), with initial datum ui(0) = u0(xi) > 0. We prove the existence and uniqueness of the solution. Moreover, we show that solutions of discrete problem converge to the continuous ones when the mesh parameter goes to zero. We also study the blow-up phenomena of solutions. For some sources f, we obtain the blow-up rate. Finally, we perform some numerical experiments. |
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