In this paper we study a Dirichlet optimal control problem for a nonlinear monotone equation with degenerate weight function and with the coefficients which we adopt as controls in L∞(Ω). Since these types of equations can exhibit the Lavrentieff phenomenon, we consider the optimal control problem in coefficients in the so-called class of H-admissible solutions. Using the direct method of calculus of variations we discuss the solvability of the above optimal control problem, and prove the attainability of H-optimal pairs via optimal solutions of some nondegenerate perturbed optimal control problems. We also introduce the concept of the Mosco-stability for the above optimal control problem and study the variational properties of Mosco-stable problems with respect to the special type of domain perturbations.
Optimal Control Problems in Coefficients for Degenerate Equations of Monotone Type: Shape Stability and Attainability Problems
D'APICE, Ciro;
2012-01-01
Abstract
In this paper we study a Dirichlet optimal control problem for a nonlinear monotone equation with degenerate weight function and with the coefficients which we adopt as controls in L∞(Ω). Since these types of equations can exhibit the Lavrentieff phenomenon, we consider the optimal control problem in coefficients in the so-called class of H-admissible solutions. Using the direct method of calculus of variations we discuss the solvability of the above optimal control problem, and prove the attainability of H-optimal pairs via optimal solutions of some nondegenerate perturbed optimal control problems. We also introduce the concept of the Mosco-stability for the above optimal control problem and study the variational properties of Mosco-stable problems with respect to the special type of domain perturbations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.