Existence of Solitary Waves in One Dimensional Peridynamics

@article{Pego2018ExistenceOS,
title={Existence of Solitary Waves in One Dimensional Peridynamics},
author={Robert L. Pego and Truong-Son Van},
journal={Journal of Elasticity},
year={2018},
pages={1-30}
}
• Published 1 February 2018
• Mathematics, Physics
• Journal of Elasticity
We give a rigorous proof of existence for solitary waves of a peridynamics model in one space dimension recently investigated by Silling (J. Mech. Phys. Solids 96:121–132, 2016). We adapt the variational framework developed by Friesecke and Wattis (Commun. Math. Phys. 161:391–418, 1994) for the Fermi-Pasta-Ulam-Tsingou lattice equations to treat a truncated problem which cuts off short-range interactions, then pass to the limit.
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