Análisis de un problema de control óptimo de fluidos dilatantes

Abstract

This paper deals with the mathematical analysis of an optimal control problem consisting of a tracking type objective function and a state equation which is a regularized version of a nonsmooth model for shear-thickening fluids. First, we study the existence of solutions of the state equation. Then, we establish the existence of minimizers for the optimal control problem. Later, we analyze the Gâteaux and Fréchet differentiability of the solution map associated to the state equation. Afterwards, we characterize the solutions of the optimal control problem by deriving an optimality system. Finally, we study the asymptotic behaviour of the considered optimal control problem as the parameter of the regularization goes to zero.