Comparison Between Solutions to the Linear Peridynamics Model and Solutions to the Classical Wave Equation

SIAM Journal on Mathematical Analysis 2026 Open access

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Authors: Giuseppe Maria Coclite, Serena Dipierro, Francesco Maddalena, Gianluca Orlando, Enrico Valdinoci
DOI: 10.1137/24m1701861
Cited by: 1
References: 31

Abstract

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 [Formula: see text] accounting for the region of influence around a material point, we prove existence and uniqueness of a solution [Formula: see text] and demonstrate the convergence of [Formula: see text] to solutions to the classical wave equation as [Formula: see text]. Moreover, we prove that the solutions to the peridynamics model with small frequency initial data are close to solutions to the classical wave equation.

Fields of Study & Subjects

Numerical methods in engineering Geotechnical Engineering and Underground Structures Electromagnetic Simulation and Numerical Methods

Publication details

Journal / source
SIAM Journal on Mathematical Analysis
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Volume
58
Issue
3
Pages
3048–3081
Publication date
19 June 2026
Language
EN