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arXiv · 2601.18355

On fractional semilinear wave equations in non-cylindrical domains

Mauro Bonafini·Van Phu Cuong Le·Riccardo Molinarolo
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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.

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Mauro Bonafini, Van Phu Cuong Le, Riccardo Molinarolo. 2026-01-26. On fractional semilinear wave equations in non-cylindrical domains. https://arxiv.org/abs/2601.18355

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