Optimal Control for a Nonlocal Model of Non-Newtonian Fluid Flows

摘要: This paper deals with an optimal control problem for a nonlocal model of the steady-state flow differential type fluid complexity 2 variable viscosity. We assume that occupies bounded three-dimensional (or two-dimensional) domain impermeable boundary. The parameter is external force. discuss both strong and weak solutions. Using one result on solvability nonlinear operator equations weak-to-weak weak-to-strong continuous mappings in Sobolev spaces, we construct solution minimizes given cost functional subject to natural conditions data. Moreover, necessary condition existence solutions derived. Simultaneously, introduce concept marginal function study its properties. In particular, it shown this system lower semicontinuous respect directed Hausdorff distance.