On fractional semilinear wave equations in non-cylindrical domains
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912853271773184 |
|---|---|
| author | Bonafini, Mauro Le, Van Phu Cuong Molinarolo, Riccardo |
| author_facet | Bonafini, Mauro Le, Van Phu Cuong Molinarolo, Riccardo |
| contents | In this paper, we investigate a class of semilinear wave equations in non-cylindrical time-dependent domains, subject to exterior homogeneous Dirichlet conditions. Under mild regularity and monotonicity assumptions on the evolving spatial domains, we establish existence of weak solutions by two different methods: a constructive time-discretization scheme and a penalty approach. The analysis applies to nonlocal fractional Laplacians and potentials with Lipschitz continuous gradient, and to vector-valued maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18355 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On fractional semilinear wave equations in non-cylindrical domains Bonafini, Mauro Le, Van Phu Cuong Molinarolo, Riccardo Analysis of PDEs 35L05, 35L85, 35Q74, 35R37, 74H20, 74K35 In this paper, we investigate a class of semilinear wave equations in non-cylindrical time-dependent domains, subject to exterior homogeneous Dirichlet conditions. Under mild regularity and monotonicity assumptions on the evolving spatial domains, we establish existence of weak solutions by two different methods: a constructive time-discretization scheme and a penalty approach. The analysis applies to nonlocal fractional Laplacians and potentials with Lipschitz continuous gradient, and to vector-valued maps. |
| title | On fractional semilinear wave equations in non-cylindrical domains |
| topic | Analysis of PDEs 35L05, 35L85, 35Q74, 35R37, 74H20, 74K35 |
| url | https://arxiv.org/abs/2601.18355 |