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.