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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 half-space, 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 e, size of the small regions r e and Robin parameter B(e). In particular, we address the convergence, as e tends to zero, of the solutions for the critical size of the small regions r e=O(e2). For certain B(e), 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.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Fuente: Zeitschrift fur Angewandte Mathematik und Physik 2022, 73(6), 234

Editorial: Springer

 Fecha de publicación: 01/12/2022

Nº de páginas: 28

Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s00033-022-01869-8

ISSN: 0044-2275,1420-9039

Proyecto español: PGC2018-098178-BBI00

Url de la publicación: https://doi.org/10.1007/s00033-022-01869-8