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Unique solvability of a crack problem with Signorini-type and Tresca friction conditions in a linearized
Takahito Kashiwabara1, Hiromichi Itou2
1Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo 153-8914, Japan.
Abstract:
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'.
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