Existence, uniqueness and homogenization of nonlinear parabolic problems with dynamical boundary conditions in perforated media
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| _version_ | 1866908715533205504 |
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| author | Anguiano, María |
| author_facet | Anguiano, María |
| contents | 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 $\varepsilon$. 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 $\varepsilon$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1712_01183 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Existence, uniqueness and homogenization of nonlinear parabolic problems with dynamical boundary conditions in perforated media Anguiano, María Analysis of PDEs 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 $\varepsilon$. 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 $\varepsilon$ 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. |
| title | Existence, uniqueness and homogenization of nonlinear parabolic problems with dynamical boundary conditions in perforated media |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1712.01183 |