Homogenization and correctors for monotone problems in cylinders of small diameter
In this paper we study the homogenization of monotone diffusion equations posed in an N-dimensional cylinder which converges to a (one-dimensional) segment line. In other terms, we pass to the limit in diffusion monotone equations posed in a cylinder whose diameter tends to zero, when simultaneously...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2013 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositório: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/139232 |
| Acesso em linha: | https://hdl.handle.net/11441/139232 https://doi.org/10.1016/J.ANIHPC.2012.10.004 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Homogenization Thin domains Monotone problems |
| Resumo: | In this paper we study the homogenization of monotone diffusion equations posed in an N-dimensional cylinder which converges to a (one-dimensional) segment line. In other terms, we pass to the limit in diffusion monotone equations posed in a cylinder whose diameter tends to zero, when simultaneously the coefficients of the equations (which are not necessarily periodic) are also varying. We obtain a limit system in both the macroscopic (one-dimensional) variable and the microscopic variable. This system is nonlocal. From this system we obtain by elimination an equation in the macroscopic variable which is local, but in contrast with usual results, the operator depends on the right-hand side of the equations. We also obtain a corrector result, i.e. an approximation of the gradients of the solutions in the strong topology of the space L^{p}L p in which the monotone operators are defined. |
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