Existence of Solutions for a Class of Impact Problems Without Viscosity

In this paper we consider dynamic frictionless impact problems of elastic materials formulated in abstract settings. The contact conditions for the impact problem are Signorini-type complementarity conditions. Using time discretization and Galerkin approximation, we investigate the convergence of numerical fully discrete trajectories to a solution of the continuous-time problem. In this way we establish the existence of solutions for a class of impact problems, some of which have been previously studied, while others have not. Most of the impact problems to which this theory can be applied are "thick" obstacle problems, although it can also be applied to a number of boundary or "thin" obstacle problems. The crucial assumption for the theory is that the cone of possible contact forces satisfies a strong pointedness condition, which can usually be related to a Sobolev embedding condition.

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