@article{Hong2023, 
author = {Desheng Hong},
title = {Blow-up of solutions for nonlinear wave equations on locally finite graphs},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {8},
pages = {18163-18173},
keywords = {blow up, nonlinear wave equation, locally finite graph},
url = {https://www.sciopen.com/article/10.3934/math.2023922},
doi = {10.3934/math.2023922},
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.}
}