Application of Rothe's method to a nonlinear wave equation on graphs

2021/08/30 by Yong Lin, Lin, Yong, Yuanyuan Xie +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.2108.12980

arxiv created 2021/08/30 · arxiv updated 2021/08/31

Abstract

We study a nonlinear wave equation on finite connected weighted 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 \citeLin-Xie 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⋅ u_t (p>1).

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