The homogenization of the heat equation with mixed conditions on randomly subsets of the boundary
We consider a domain in RN , N ≥ 3, such that a portion of its boundary is plane. In this portion we fix a sequence Kε of small subsets randomly distributed in such way that the distance between them is of order ε and their diameters are of order εN−1/N−2 . We study the asymptotic behavior of the he...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:dnet:idus________::40e6726c4565a5c0eeeb57a52c8f5262 |
| Acceso en línea: | https://hdl.handle.net/11441/186033 https://doi.org/10.3934/proc.2013.2013.85 |
| Access Level: | acceso abierto |
| Palabra clave: | Homogenization linear problems random perforated domains |
| Sumario: | We consider a domain in RN , N ≥ 3, such that a portion of its boundary is plane. In this portion we fix a sequence Kε of small subsets randomly distributed in such way that the distance between them is of order ε and their diameters are of order εN−1/N−2 . We study the asymptotic behavior of the heat equation with Dirichlet conditions on Kε and Neumann conditions on the rest of the boundary. We prove the convergence to a limit problem with a Fourier-Robin boundary condition which has the physical interest of being deterministic. |
|---|