Bibliographic Details
| Title: |
Comparison between solutions to the linear peridynamics model and solutions to the classical wave equation |
| Authors: |
Coclite, Giuseppe Maria, Dipierro, Serena, Maddalena, Francesco, Orlando, Gianluca, Valdinoci, Enrico |
| Publication Year: |
2024 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Analysis of PDEs, 74A70, 74B10, 70G70, 35L05 |
| More Details: |
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. |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2410.09211 |
| Accession Number: |
edsarx.2410.09211 |
| Database: |
arXiv |
