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Research Article | Open Access

Blow-up of solutions for nonlinear wave equations on locally finite graphs

School of Mathematics, Renmin University of China, Beijing 100872, China
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Abstract

Let G = ( V , E ) be a local finite connected weighted graph, Ω be a finite subset of V satisfying Ω ∘ ≠ ∅. In this paper, we study the nonexistence of the nonlinear wave equation

∂ t 2 u = Δ u + f ( u )

on G. Under the appropriate conditions of initial values and nonlinear term, we prove that the solution for nonlinear wave equation blows up in a finite time. Furthermore, a numerical simulation is given to verify our results.

Keywords

nonlinear wave equationblow uplocally finite graph
CLC number: 35L05, 35R02, 58J45

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AIMS Mathematics
Volume 8 Issue 8,
August 2023
Pages 18163-18173
DOI: 10.3934/math.2023922

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Cite this article:
Hong D. Blow-up of solutions for nonlinear wave equations on locally finite graphs. AIMS Mathematics, 2023, 8(8): 18163-18173. https://doi.org/10.3934/math.2023922

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Received: 23 February 2023
Revised: 14 May 2023
Accepted: 16 May 2023
Published: 15 August 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)