Comparison Between Solutions to the Linear Peridynamics Model and Solutions to the Classical Wave Equation
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 $δ>0$ accounting for the region of influence around a material point, we prove existence and uniqueness of a solution $u_δ$ and demonstrate the convergence of $u_δ$ to solutions to the classical wave equation as $δ\to 0$. Moreover, we prove that the solutions to the peridynamics model with small frequency initial data are close to solutions to the classical wave equation.
Authors
- Serena Dipierro (ORCID: https://orcid.org/0000-0003-4386-4485)
- Giuseppe Maria Coclite (ORCID: https://orcid.org/0000-0001-6019-4757)
- Gianluca Orlando (ORCID: https://orcid.org/0000-0002-8283-4804)
- Enrico Valdinoci (ORCID: https://orcid.org/0000-0001-6222-2272)
- Francesco Maddalena (ORCID: https://orcid.org/0000-0003-2862-1960)
Institutions
- The University of Western Australia (AU)
- Polytechnic University of Bari (IT)
Publication Details
- Journal
- SIAM Journal on Mathematical Analysis
- Published
- 2026-06-19
- DOI
- https://doi.org/10.1137/24m1701861
- Citations
- 1
- Primary Topic
- Numerical methods in engineering
- Type
- preprint
- Field-Weighted Citation Impact
- 0.00
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- European Commission
- Ministero dell’Istruzione, dell’Università e della Ricerca
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
- Australian Research Council