Nonexistence results for the semilinear wave equation on graphs

TL;DR

This paper studies the semilinear wave equation on weighted graphs, providing conditions under which solutions do not exist globally, and introduces a new technique for analyzing sign-changing solutions.

Contribution

It offers new nonexistence results for solutions of the wave equation on graphs, including a novel method for sign-changing solutions.

Findings

Sufficient conditions for nonexistence of global solutions

Results applicable to both nonnegative and sign-changing solutions

Introduction of a new technique for sign-changing solution analysis

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.