Comparison between solutions to the linear peridynamics model and solutions to the classical wave equation

2024/10/11 by Coclite, Giuseppe Maria, Dipierro, Serena, Maddalena, Francesco +2
#35L05 #70G70 #74A70 #74B10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.09211

Abstract

In this paper, we consider an equation inspired by linear peridynamics and we establish its connection with the classical wave equation. In particular, given a horizon δ>0 accounting for the region of influence around a material point, we prove existence and uniqueness of a solution u_δ and demonstrate the convergence of u_δ to solutions to the classical wave equation as δ→ 0. Moreover, we prove that the solutions to the peridynamics model with small frequency initial data are close to solutions to the classical wave equation.

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