Calculus of Variations and Geometric Measure Theory

G. M. Coclite - S. Dipierro - F. Maddalena - G. Orlando - E. Valdinoci

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

created by orlando on 19 Oct 2024

[BibTeX]

preprint

Inserted: 19 oct 2024

Year: 2024

ArXiv: 2410.09211 PDF

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.