We consider the problem of frictional contact between an piezoelectric body and a
conductive foundation. The electro-elastic constitutive law is assumed to be nonlinear and
the contact is modelled with the Signorini condition, nonlocal Coulomb friction law and a
regularized electrical conductivity condition. The existence of a unique weak solution of
the model is established. The finite elements approximation for the problem is presented,
and error...
We study an evolution problem which describes the quasistatic contact of a viscoelastic body with a foundation. We model the contact with normal damped response and a local friction law. We derive a variational formulation of the model and we establish the existence of a unique weak solution to the problem. The proof is based on monotone operators and fixed point arguments. We also establish the continuous dependence of the solution on the contact boundary conditions.
In this work, we consider an inverse backward problem for a nonlinear parabolic equation of the Burgers' type with a memory term from final data. To this aim, we first establish the well-posedness of the direct problem. On the basis of the optimal control framework, the existence and necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability of the minimizer are deduced from the necessary condition. Numerical experiments demonstrate the effectiveness...
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