Existence and uniqueness of weak solutions to a parabolic nonlocal 1-Laplacian equation
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914850453585920 |
|---|---|
| author | Li, Dingding Zhang, Chao |
| author_facet | Li, Dingding Zhang, Chao |
| contents | We consider a class of parabolic nonlocal $1$-Laplacian equation \begin{align*} u_t+(-Δ)^s_1u=f \quad \text{ in }Ω\times(0,T]. \end{align*} By employing the Rothe time-discretization method, we establish the existence and uniqueness of weak solutions to the equation above. In particular, different from the previous results on the local case, we infer that the weak solution maintains $\frac{1}{2}$-Hölder continuity in time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19020 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and uniqueness of weak solutions to a parabolic nonlocal 1-Laplacian equation Li, Dingding Zhang, Chao Analysis of PDEs We consider a class of parabolic nonlocal $1$-Laplacian equation \begin{align*} u_t+(-Δ)^s_1u=f \quad \text{ in }Ω\times(0,T]. \end{align*} By employing the Rothe time-discretization method, we establish the existence and uniqueness of weak solutions to the equation above. In particular, different from the previous results on the local case, we infer that the weak solution maintains $\frac{1}{2}$-Hölder continuity in time. |
| title | Existence and uniqueness of weak solutions to a parabolic nonlocal 1-Laplacian equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.19020 |