Yong LinYau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, ChinaYuanyuan XieSchool of Mathematics, Renmin University of China, Beijing, 100872, China
Analysis of PDEsmathscidoc:2207.03011
arXiv, 2021.8
Let G=(V,E) be a finite weighted graph, and Ω⊆V be a domain such that Ω^∘≠∅. In this paper, we study the following initial boundary problem for the non-homogenous wave equation
∂^2_t u(t,x) − Δ_Ω u(t,x) = f(t,x), (t,x)∈[0,∞)×Ω^∘
u(0,x)=g(x), x∈Ω^∘,
∂_t u(0,x)=h(x), x∈Ω^∘,
u(t,x)=0, (t,x)∈[0,∞)×∂Ω,
where Δ_Ω denotes the Dirichlet Laplacian on Ω^∘. Using Rothe's method, we prove that the above wave equation has a unique solution.
@inproceedings{yong2021the,
title={The existence of the solution of the wave equation on graphs},
author={Yong Lin, and Yuanyuan Xie},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707161226414216582},
booktitle={arXiv},
year={2021},
}
Yong Lin, and Yuanyuan Xie. The existence of the solution of the wave equation on graphs. 2021. In arXiv. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707161226414216582.