Nonexistence results for the semilinear wave equation on graphs
Analysis of PDEs
2025-06-18 v2
Abstract
We investigate the semilinear wave equation with potential on weighted graphs. We establish sufficient conditions for the nonexistence of global-in-time solutions. Both nonnegative and sign-changing solutions are considered. In particular, the proof for sign-changing solutions relies on a novel technique for this type of result.
Keywords
Cite
@article{arxiv.2506.08697,
title = {Nonexistence results for the semilinear wave equation on graphs},
author = {Dario Daniele Monticelli and Fabio Punzo and Jacopo Somaglia},
journal= {arXiv preprint arXiv:2506.08697},
year = {2025}
}