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Publication 18-CNA-001

Existence of solitary waves in one dimensional peridynamics

Truong-Son Van
Department of Mathematical Sciences and Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA 15213, USA

Robert L. Pego
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

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 96:121-32, 2016). We adapt the variational framework developed by Friesecke and Wattis (Comm. 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.

Get the paper in its entirety as  18-CNA-001.pdf

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