A rational model of a dynamical contact of a viscoelastic body with its support is presented. It is assumed that the contact is frictionless and permits a limited interpenetration which is prescribed. A weak formulation of the problem is given and the existence of its solutions is proved. It is also shown that if the depth of the interpenetration tends to zero, the solutions converge to a solution of the Signorini contact (without interpenetration).
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