A gradient flow for the Porous Medium Equations with Dirichlet boundary conditions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866908383539363840 |
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| author | Kim, Dongkwang Koo, Dowan Seo, Geuntaek |
| author_facet | Kim, Dongkwang Koo, Dowan Seo, Geuntaek |
| contents | We consider the gradient flow structure of the porous medium equations with non-negative constant Dirichlet boundary conditions. We construct weak solutions to the equations via the minimizing movement scheme by considering an entropy functional with respect to $Wb_2$ distance, which is a modified Wasserstein distance introduced by Figalli and Gigli [J. Math. Pures Appl. 94, (2010), pp. 107-130]. Furthermore, the constructed solutions are characterized as curves of maximal slope in a suitable sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_06092 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A gradient flow for the Porous Medium Equations with Dirichlet boundary conditions Kim, Dongkwang Koo, Dowan Seo, Geuntaek Analysis of PDEs Optimization and Control 35A15, 49K20, 49Q22 We consider the gradient flow structure of the porous medium equations with non-negative constant Dirichlet boundary conditions. We construct weak solutions to the equations via the minimizing movement scheme by considering an entropy functional with respect to $Wb_2$ distance, which is a modified Wasserstein distance introduced by Figalli and Gigli [J. Math. Pures Appl. 94, (2010), pp. 107-130]. Furthermore, the constructed solutions are characterized as curves of maximal slope in a suitable sense. |
| title | A gradient flow for the Porous Medium Equations with Dirichlet boundary conditions |
| topic | Analysis of PDEs Optimization and Control 35A15, 49K20, 49Q22 |
| url | https://arxiv.org/abs/2212.06092 |