Shape stability of optimal control problems in coefficients for coupled system of Hammerstein type
Olha P. Kupenko, Rosanna Manzo · Discrete and Continuous Dynamical Systems - B · 2015
In this paper we consider an optimal controlproblem (OCP) for the coupled system of a nonlinear monotone Dirichlet problem with matrix-valued $L^\infty(\Omega;\mathbb{R}^{N\times N} )$-controls in coefficients and a nonlinear equation of Hammerstein type. Since problemsof this type have no solutions in general, we make a specialassumption on the coefficients of the state equation and introducethe class of so-called solenoidal admissible controls. Using the directmethod in calculus of variations, we prove the existence of an optimal control. We also study the stability of theoptimal control problem with respect to the domain perturbation. In particular, we derive the sufficient conditionsof the Mosco-stability for the given class of OCPs.