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In this paper we consider an optimal control problem (OCP) for the coupledsystem of a nonlinear monotone Dirichlet problem with matrix- valued non-smoothcontrols in coefficients and a nonlinear equation of Ham- merstein type. Sinceproblems of this type have no solutions in general, we make a specialassumption on the coefficients of the state equation and in- troduce the classof so-called solenoidal admissible controls. Using the direct method incalculus of variations, we prove the existence of an optimal control. We alsostudy the stability of the optimal control problem with respect to the domainperturbation. In particular, we derive the sufficient conditions of theMosco-stability for the given class of OCPs.

Shape stability of optimal control problems in coefficients for coupled system of Hammerstein type