Global well-posedness for a time-fractional doubly nonlinear equation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911111084769280 |
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| author | Akagi, Goro Sodini, Giacomo Enrico Stefanelli, Ulisse |
| author_facet | Akagi, Goro Sodini, Giacomo Enrico Stefanelli, Ulisse |
| contents | We consider a time-fractional parabolic equation of doubly nonlinear type, featuring nonlinear terms both inside and outside the differential operator in time. The main nonlinearities are maximal monotone graphs, without restrictions on the growth. In addition, a Lipschitz continuous perturbation is considered. The existence of global weak solutions is obtained via a regularization and Galerkin approximation method. Uniqueness is also discussed under some additional assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13694 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global well-posedness for a time-fractional doubly nonlinear equation Akagi, Goro Sodini, Giacomo Enrico Stefanelli, Ulisse Analysis of PDEs 35K55 We consider a time-fractional parabolic equation of doubly nonlinear type, featuring nonlinear terms both inside and outside the differential operator in time. The main nonlinearities are maximal monotone graphs, without restrictions on the growth. In addition, a Lipschitz continuous perturbation is considered. The existence of global weak solutions is obtained via a regularization and Galerkin approximation method. Uniqueness is also discussed under some additional assumptions. |
| title | Global well-posedness for a time-fractional doubly nonlinear equation |
| topic | Analysis of PDEs 35K55 |
| url | https://arxiv.org/abs/2508.13694 |