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

Let G = (V, E) be a local finite connected weighted graph, n be a finite subset of V satisfying n degrees # 0. In this paper, we study the nonexistence of the nonlinear wave equation a2t u = Delta 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.