Modified Wasserstein gradient flow formulation of time-fractional porous medium equations with nonlocal pressure
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916391859257344 |
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| author | Chung, Nhan-Phu Trinh, Thanh-Son |
| author_facet | Chung, Nhan-Phu Trinh, Thanh-Son |
| contents | We consider a class of time-fractional porous medium equations with nonlocal pressure. We show the existence of their weak solutions by proposing a JKO scheme for modified Wasserstein distance and a square fractional Sobolev norm. Moreover, the regularization effect and the Lp norm estimate are established in this paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08441 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modified Wasserstein gradient flow formulation of time-fractional porous medium equations with nonlocal pressure Chung, Nhan-Phu Trinh, Thanh-Son Analysis of PDEs We consider a class of time-fractional porous medium equations with nonlocal pressure. We show the existence of their weak solutions by proposing a JKO scheme for modified Wasserstein distance and a square fractional Sobolev norm. Moreover, the regularization effect and the Lp norm estimate are established in this paper. |
| title | Modified Wasserstein gradient flow formulation of time-fractional porous medium equations with nonlocal pressure |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.08441 |