On switching points of optimal controls for coercive parabolic boundary control problems

Abstract

In this paper, a parabolic boundary control problem with linear state equation and quadratic coercive objective functional is considered. It is shown, how the optimal control depends on the regularization parameter ν < 0, which is responsible for the coercivity of the objective functional. A new notion of switching points is introduced and their convergence for ν → + 0 is investigated. Numerical examples illustrate the theory.

Keywords:

• Parabolic boundary control problem
• linear state equations
• quadratic coercive objective functional
• regularization
• switching points

AMS 1980 Subject Classifications:

• Primary: 49 A 22
• Secondary: 49 B 22
• Secondary: 49 A 36
• Secondary: 55 N 99