Well-posedness of the peridynamic model with Lipschitz continuous pairwise force function

Peridynamics is a nonlocal theory of continuum mechanics based on a, in general, nonlinear integro-differential equation without spatial derivatives. Well-posedness of the nonlinear multidimensional peridynamic initial value problem under the assumption of (local) Lipschitz-type continuity of the pairwise force function with respect to the difference in the deformation is shown.

Keywords

nonlocal continuum mechanics, nonlinear elasticity, peridynamics, abstract ordinary differential equation, well-posedness, maximal solution

2010 Mathematics Subject Classification

34G20, 35Q74, 35R09, 74B20, 74H20, 74H40

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Published 15 June 2013