Unique solvability of a crack problem with Signorini-type and Tresca friction conditions in a linearized elastodynamic body.

We consider dynamic motion of a linearized elastic body with a crack subject to a modified contact law, which we call the Signorini contact condition of dynamic type , and to the Tresca friction condition. Whereas the modified contact law involves both displacement and velocity, it formally includes the usual non-penetration condition as a special case. We prove that there exists a unique strong solution to this model. It is remarkable that not only existence but also uniqueness is obtained and that no viscosity term that serves as a parabolic regularization is added in our model. This article is part of the theme issue 'Non-smooth variational problems and applications'.