On $p$-Laplacian reaction-diffusion problems with dynamical boundary conditions in perforated media
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866912769398276096 |
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| author | Anguiano, María |
| author_facet | Anguiano, María |
| contents | This paper deals with the homogenization of the $p$-Laplacian reaction-diffusion problems in a domain containing periodically distributed holes of size $\varepsilon$, with a dynamical boundary condition of pure-reactive type. We generalize our previous results established in the case where the diffusion is modeled by the Laplacian operator, i.e., with $p=2$. We prove the convergence of the homogenization process to a nonlinear $p$-Laplacian reaction-diffusion equation 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_14960 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On $p$-Laplacian reaction-diffusion problems with dynamical boundary conditions in perforated media Anguiano, María Analysis of PDEs This paper deals with the homogenization of the $p$-Laplacian reaction-diffusion problems in a domain containing periodically distributed holes of size $\varepsilon$, with a dynamical boundary condition of pure-reactive type. We generalize our previous results established in the case where the diffusion is modeled by the Laplacian operator, i.e., with $p=2$. We prove the convergence of the homogenization process to a nonlinear $p$-Laplacian reaction-diffusion equation 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. |
| title | On $p$-Laplacian reaction-diffusion problems with dynamical boundary conditions in perforated media |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2006.14960 |