Weighted Energy-Dissipation approach to semilinear gradient flows with state-dependent dissipation
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911827704676352 |
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| author | Akagi, Goro Stefanelli, Ulisse Voso, Riccardo |
| author_facet | Akagi, Goro Stefanelli, Ulisse Voso, Riccardo |
| contents | We investigate the Weighted Energy-Dissipation variational approach to semilinear gradient flows with state-dependent dissipation. A family of parameter-dependent functionals defined over entire trajectories is introduced and proved to admit global minimizers. These global minimizers correspond to solutions of elliptic-in-time regularizations of the limiting causal problem. By passing to the limit in the parameter we prove that such global minimizers converge, up to subsequences, to a solution of the gradient flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03370 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weighted Energy-Dissipation approach to semilinear gradient flows with state-dependent dissipation Akagi, Goro Stefanelli, Ulisse Voso, Riccardo Analysis of PDEs 35K90, 47J30, 47J35, 58E30 We investigate the Weighted Energy-Dissipation variational approach to semilinear gradient flows with state-dependent dissipation. A family of parameter-dependent functionals defined over entire trajectories is introduced and proved to admit global minimizers. These global minimizers correspond to solutions of elliptic-in-time regularizations of the limiting causal problem. By passing to the limit in the parameter we prove that such global minimizers converge, up to subsequences, to a solution of the gradient flow. |
| title | Weighted Energy-Dissipation approach to semilinear gradient flows with state-dependent dissipation |
| topic | Analysis of PDEs 35K90, 47J30, 47J35, 58E30 |
| url | https://arxiv.org/abs/2404.03370 |