Nonexistence results for the semilinear wave equation on graphs

2025/06/10 by Dario D. Monticelli, Monticelli, Dario Daniele, Fabio Punzo +3 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2506.08697

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.

Citations

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Cited by

• Blow up results and lifespan estimates for nonlinear damped wave equations on weighted graphs

Related

• Nonexistence of solutions to parabolic problems with a potential on weighted graphs
• Nonexistence results for semilinear elliptic equations on weighted graphs
• The existence of the solution of the wave equation on graphs
• Application of Rothe's method to a nonlinear wave equation on graphs
• Nonexistence Results for a General Class of Parabolic Problems with a Potential on Weighted Graphs