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

Yong Lin; Yuanyuan Xie

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

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arxiv 2108.12980 v1 pith:2J2MTGMR submitted 2021-08-30 math.AP

Yong Lin , Yuanyuan Xie This is my paper · ORCID

classification math.AP

keywords equationwavegraphsnonlinearexistencerothesolutionuniqueness

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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 \cite{Lin-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 $|u_t|^{p-1}\cdot u_t$ ($p>1$).

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