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arXiv · 2410.09211

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

Giuseppe Maria Coclite·Serena Dipierro·Francesco Maddalena·Gianluca Orlando·Enrico Valdinoci
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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.

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Giuseppe Maria Coclite, Serena Dipierro, Francesco Maddalena, Gianluca Orlando, Enrico Valdinoci. 2024-10-11. Comparison between solutions to the linear peridynamics model and solutions to the classical wave equation. https://arxiv.org/abs/2410.09211

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