Almost Finite Speed of Propagation for Linear Peridynamics

TL;DR

This paper demonstrates that in one-dimensional linear peridynamics, solutions exhibit decay estimates similar to wave equations, indicating an almost finite speed of propagation despite the non-finite speed nature of the model.

Contribution

It establishes decay estimates for solutions of 1D linear peridynamics, showing an almost finite speed of propagation analogous to classical wave equations.

Findings

Solutions decay away from initial data domain

Derivatives of solutions also decay

Approximate finite speed of propagation established

Abstract

The peridynamic analogue of the wave equation does not have finite speed propogation. We show, for one dimensional linear peridynamics, that solutions do nonetheless satisfy estimates analogous to those satisfied by solutions of the wave equations. More precisely, the solution and all derivatives become small as we go away from the domain of dependence of the initial data.