On fractional semilinear wave equations in non-cylindrical domains
Analysis of PDEs
2026-01-28 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2601.18355,
title = {On fractional semilinear wave equations in non-cylindrical domains},
author = {Mauro Bonafini and Van Phu Cuong Le and Riccardo Molinarolo},
journal= {arXiv preprint arXiv:2601.18355},
year = {2026}
}