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Existence of Solitary Waves in One Dimensional Peridynamics

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Abstract

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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Acknowledgements

T.-S. Van would like to thank Gautam Iyer and Hung V. Tran for encouragement and useful comments. This material is based upon work partially supported by the National Science Foundation under grants DMS-1515400 and DMS-1812609, the Simons Foundation under grant #395796, and the Center for Nonlinear Analysis, through NSF grant OISE-0967140.

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  1. Department of Mathematical Sciences and Center for Nonlinear Analysis, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Robert L. Pego & Truong-Son Van

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  1. Robert L. Pego
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  2. Truong-Son Van
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Correspondence to Truong-Son Van.

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Pego, R.L., Van, TS. Existence of Solitary Waves in One Dimensional Peridynamics. J Elast 136, 207–236 (2019). https://doi.org/10.1007/s10659-018-9701-6

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  • DOI: https://doi.org/10.1007/s10659-018-9701-6

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