Time-fractional gradient flows for nonconvex energies in Hilbert spaces
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916566246883328 |
|---|---|
| author | Akagi, Goro Nakajima, Yoshihito |
| author_facet | Akagi, Goro Nakajima, Yoshihito |
| contents | This article is devoted to presenting an abstract theory on time-fractional gradient flows for nonconvex energy functionals in Hilbert spaces. Main results consist of local and global in time existence of (continuous) strong solutions to time-fractional evolution equations governed by the difference of two subdifferential operators in Hilbert spaces. To prove these results, fractional chain-rule formulae, a Lipschitz perturbation theory for convex gradient flows and Gronwall-type lemmas for nonlinear Volterra integral inequalities are developed. They also play a crucial role to cope with the lack of continuity (in time) of energies due to the subdiffusive nature of the issue. Moreover, the abstract theory is applied to the Cauchy-Dirichlet problem for some $p$-Laplace subdiffusion equations with blow-up terms complying with the so-called Sobolev (sub)critical growth condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08059 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-fractional gradient flows for nonconvex energies in Hilbert spaces Akagi, Goro Nakajima, Yoshihito Analysis of PDEs 47J35, 35K61 This article is devoted to presenting an abstract theory on time-fractional gradient flows for nonconvex energy functionals in Hilbert spaces. Main results consist of local and global in time existence of (continuous) strong solutions to time-fractional evolution equations governed by the difference of two subdifferential operators in Hilbert spaces. To prove these results, fractional chain-rule formulae, a Lipschitz perturbation theory for convex gradient flows and Gronwall-type lemmas for nonlinear Volterra integral inequalities are developed. They also play a crucial role to cope with the lack of continuity (in time) of energies due to the subdiffusive nature of the issue. Moreover, the abstract theory is applied to the Cauchy-Dirichlet problem for some $p$-Laplace subdiffusion equations with blow-up terms complying with the so-called Sobolev (sub)critical growth condition. |
| title | Time-fractional gradient flows for nonconvex energies in Hilbert spaces |
| topic | Analysis of PDEs 47J35, 35K61 |
| url | https://arxiv.org/abs/2501.08059 |