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
sonv@andrew.cmu.edu

Robert L. Pego
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
rpego@andrew.cmu.edu

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.

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