Nonlocal doubly nonlinear diffusion problems with nonlinear boundary conditions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866916255594708992 |
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| author | Solera, Marcos Toledo, Julián |
| author_facet | Solera, Marcos Toledo, Julián |
| contents | We study the existence and uniqueness of mild and strong solutions of nonlocal nonlinear diffusion problems of $p$-Laplacian type with nonlinear boundary conditions posed in metric random walk spaces. These spaces include, among others, weighted discrete graphs and $\mathbb{R}^N$ with a random walk induced by a nonsingular kernel. We also study the case of nonlinear dynamical boundary conditions. The generality of the nonlinearities considered allow us to cover the nonlocal counterparts of a large scope of local diffusion problems: Stefan problems, Hele-Shaw problems, diffusion in porous media problems, obstacle problems, and more. Nonlinear semigroup theory is the basis for this study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_00340 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Nonlocal doubly nonlinear diffusion problems with nonlinear boundary conditions Solera, Marcos Toledo, Julián Analysis of PDEs 35K55, 47H06, 47J35 We study the existence and uniqueness of mild and strong solutions of nonlocal nonlinear diffusion problems of $p$-Laplacian type with nonlinear boundary conditions posed in metric random walk spaces. These spaces include, among others, weighted discrete graphs and $\mathbb{R}^N$ with a random walk induced by a nonsingular kernel. We also study the case of nonlinear dynamical boundary conditions. The generality of the nonlinearities considered allow us to cover the nonlocal counterparts of a large scope of local diffusion problems: Stefan problems, Hele-Shaw problems, diffusion in porous media problems, obstacle problems, and more. Nonlinear semigroup theory is the basis for this study. |
| title | Nonlocal doubly nonlinear diffusion problems with nonlinear boundary conditions |
| topic | Analysis of PDEs 35K55, 47H06, 47J35 |
| url | https://arxiv.org/abs/2103.00340 |