Existence, Uniqueness and Homogenization of Nonlinear Parabolic Problems with Dynamical Boundary Conditions in Perforated Media
We consider a nonlinear parabolic problem with nonlinear dynamical boundary conditions of pure-reactive type in a media perforated by periodically distributed holes of size . The novelty of our work is to consider a nonlinear model where the nonlinearity also appears in the boundary. The existence a...
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| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2019 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/153756 |
| Online Access: | https://hdl.handle.net/11441/153756 https://doi.org/10.1007/s00009-019-1459-y |
| Access Level: | Open access |
| Keyword: | Homogenization perforated media dynamical boundary conditions |
| Summary: | We consider a nonlinear parabolic problem with nonlinear dynamical boundary conditions of pure-reactive type in a media perforated by periodically distributed holes of size . The novelty of our work is to consider a nonlinear model where the nonlinearity also appears in the boundary. The existence and uniqueness of solution is analyzed. Moreover, passing to the limit when goes to zero, a new nonlinear parabolic problem defined on a unified domain without holes with zero Dirichlet boundary condition and with extra terms coming from the influence of the nonlinear dynamical boundary conditions is rigorously derived. |
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