| Abstract: |
| In the talk a class of elliptic quasi-variational-hemivariational inequalities with constraints is examined. The existence of solutions and compactness of the solution set is proved. The upper semicontinuity property of the solution set with respect to a parameter appearing in the data is also established. Then, the results are applied to the stationary incompressible Navier-Stokes equation
with mixed multivalued boundary conditions which model a generalized Newtonian fluid of Bingham-type. The corresponding boundary value problem involves a nonmonotone version of the slip condition of frictional type described by the Clarke subgradient law with a locally Lipschitz potential and an implicit obstacle constraint set. Finally, within the framework of optimal control, a double minimization problem for the fluid model is studied and the existence of its solution is established. |
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