Bulletin of the
Korean Mathematical Society BKMS

We study a nonlinear wave equation on finite connected weig\-hted graphs. Using Rothe's and energy methods, we prove the existence and uniqueness of solution under certain assumption. For linear wave equation on graphs, Lin and Xie [10] obtained the existence and uniqueness of solution. The main novelty of this paper is that the wave equation we considered has the nonlinear damping term $|u_t|^{p-1}\cdot u_t$ ($p>1$).

Keywords: Rothe's method, nonlinear wave equation, graph

MSC numbers: Primary 35L05, 35R02, 58J45

Supported by: This work is supported by the National Science Foundation of China [12071245].