SHAPE STABILITY OF OPTIMAL CONTROL PROBLEMS IN COEFFICIENTS FOR COUPLED SYSTEM OF HAMMERSTEIN TYPE

Abstract

In this paper we consider an optimal control problem (OCP) for the coupledsystem of a nonlinear monotone Dirichlet problem with matrix-valued L∞(Ω;RN×N)-controls in coecients and a nonlinear equation of Hammerstein type, where solution nonlinearly depends on L∞ -control. Since problems of this type have no solutions in general, we make a special assumption on the coecients of the state equations and introduce the class of so-called solenoidal admissible controls. Using the direct method in calculus of variations, we prove the existence of an optimal control. We also study the stability of the optimal control problem with respect to the domain perturbation. In particular, we derive the sucient conditions of the Mosco-stability for the given class of OCPs.

Keywords

• nonlinear monotone Dirichlet problem
• equation of Hammerstein type
• control in coecients
• domain perturbation