An inverse problem for Bingham type fluids

In this paper we study a coefficient identification problem described by an elliptic variational-hemivariational inequality with unilateral constraints. The inequality is the weak formulation of the mathematical model of a stationary incompressible flow of Bingham type in a bounded domain. The unknown coefficient is a generalized viscosity function of the fluid. The boundary conditions represent generalizations of the no leak condition and a multivalued and nonmonotone version of a nonlinear Navier–Fujita frictional slip condition. The result on well posedness of the direct problem is established based on the theory of multivalued pseudomonotone operators. The existence to the inverse problem is proved by a Weierstrass type argument.