Lipschitz stability of solutions to linear-quadratic parabolic control problems with respect to perturbations

• Main Author: Tröltzsch, F.
• Language: English
• Published: Technische Universität Chemnitz 1998
• Subjects: info:eu-repo/classification/ddc/510; ddc:510; Boundary control; distributed control; linear parabolic equation; control constraints; Lipschitz continuity; supremum norm; MSC 49K20; MSC 49K40
• Online Access: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801229; https://monarch.qucosa.de/id/qucosa%3A17498; https://monarch.qucosa.de/api/qucosa%3A17498/attachment/ATT-0/; https://monarch.qucosa.de/api/qucosa%3A17498/attachment/ATT-1/; https://monarch.qucosa.de/api/qucosa%3A17498/attachment/ATT-2/

We consider a class of control problems governed by a linear parabolic initial-boundary value problem with linear-quadratic objective and pointwise constraints on the control. The control system contains different types of perturbations. They appear in the linear part of the objective functional, in the right hand side of the equation, in its boundary condition, and in the initial value. Making use of parabolic regularity in the whole scale of $L^p$ the known Lipschitz stability in the $L^2$-norm is improved to the supremum-norm.