*preprint*

**Inserted:** 19 oct 2024

**Year:** 2024

**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.