Optimal Feedback Control for a Thermoviscoelastic Model of the Motion of Water Polymer Solutions

We study an optimal feedback control problem for an initial boundary value problem of a thermoviscoelastic model describing the motion of weakly concentrated water polymer solutions in the presence of dependence of the viscosity on the temprature. We prove the existence of an optimal solution minimizing to a given bounded lower semicontinuous quality functional. For proving the existence of an optimal solution, we use the topological approximation method for studying problems in hydrodynamics. © 2019, Allerton Press, Inc.