On relaxation of state-constrained optimal control problem in coefficients for biharmonic equation

Abstract

We study a Dirichlet optimal control problem for biharmonic equation withcontrol and state constraints. The coecient of the biharmonic operator, the weightu, we take as a control in L1(Ω). We discuss the relaxation approach and show thatsome optimal solutions to the original problem can be attained in the limit byoptimal solutions of some extremal problem for variational inequality with a specialpenalized cost functional.

Keywords

• biharmonic problem
• optimal control
• control in coecients
• relaxation
• existence result