Boundary homogenization with large reaction terms on a strainer-type wall
ABSTRACT: We consider a homogenization problem for the Laplace operator posed in a bounded domain of the upper halfspace, a part of its boundary being in contact with the plane {x3 = 0}. On this part, the boundary conditions alternate from Neumann to nonlinear-Robin, being of Dirichlet type outside....
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/26346 |
| Acceso en línea: | https://hdl.handle.net/10902/26346 |
| Access Level: | acceso abierto |
| Palabra clave: | Boundary homogenization Local problems Extended capacity Critical relations Laplace operator |
| Sumario: | ABSTRACT: We consider a homogenization problem for the Laplace operator posed in a bounded domain of the upper halfspace, a part of its boundary being in contact with the plane {x3 = 0}. On this part, the boundary conditions alternate from Neumann to nonlinear-Robin, being of Dirichlet type outside. The nonlinear-Robin boundary conditions are imposed on small regions periodically placed along the plane and contain a Robin parameter that can be very large. We provide all the possible homogenized problems, depending on the relations between the three parameters: period ε, size of the small regions rε and Robin parameter β(ε). In particular, we address the convergence, as ε tends to zero, of the solutions for the critical size of the small regions rε = O(ε2). For certain β(ε), a nonlinear capacity term arises in the strange term which depends on the macroscopic variable and allows us to extend the usual capacity definition to semilinear boundary conditions. |
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