Bull. Korean Math. Soc. 2022; 59(3): 745-756
Online first article May 31, 2022 Printed May 31, 2022
https://doi.org/10.4134/BKMS.b210445
Copyright © The Korean Mathematical Society.
Yong Lin, Yuanyuan Xie
Tsinghua University; Renmin University of China
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].
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