Published Paper

Inserted: 19 oct 2024
Last Updated: 19 sep 2026

Journal: SIAM J. Math. Anal.
Volume: 58
Number: 3
Pages: 3048 - 3081
Year: 2026
Doi: https://doi.org/10.1137/24M1701861

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 $\delta>0$ accounting for the region of influence around a material point, we prove existence and uniqueness of a solution $u_\delta$ and demonstrate the convergence of $u_\delta$ to solutions to the classical wave equation as $\delta \to 0$. Moreover, we prove that the solutions to the peridynamics model with small frequency initial data are close to solutions to the classical wave equation.