2019/08/06 by Yong Lin, Lin, Yong, Yuanyuan Xie +1 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #math.AP
paper · pdf · doi:10.48550/arxiv.1908.02137
openalex publication_date 2019/08/06 · arxiv created 2021/08/30 · arxiv updated 2021/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \ \beginaligned ∂t2 u(t,x)-ΔΩu(t,x)=f(t,x), &(t,x)∈[0,∞)× Ω^∘,
u(0,x)=g(x), & x∈Ω^∘,
∂tu(0,x)=h(x), & x∈Ω^∘,
u(t,x)=0, &(t,x)∈[0,∞)×∂ Ω, \endaligned . where ΔΩ denotes the Dirichlet Laplacian on Ω^∘. Using Rothe's method, we prove that the above wave equation has a unique solution.