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Using a general theory for evolution inclusions, existence and uniqueness theorems are obtained for weak solutions to a frictional dynamic contact problem for elastic visco-plastic material. An existence theorem in the case where the friction coefficient is discontinuous is also presented.
We prove the existence of solutions for the implicit evolution inclusion (B(t)u(t)) + A(t, u(t)) f (t) under conditions that are easy to verify on the set valued operator A(t, ·) and that do not imply the operator is monotone. We also present an example where our existence theorem applies to a time dependent implicit inclusion.
The mathematical theory of quasistatic elastic viscoplastic models with damage is studied. The existence of the unique local weak solution is established by using approximate problems and a priori estimates. Point-wise estimates on the damage are obtained using a new comparison technique which removes the necessity of including a subgradient term in the… (More)