New assumptions for stability analysis in elliptic optimal control problems

Abstract

This paper is dedicated to the stability analysis of the optimal solutions of a control problem associated with a semilinear elliptic equation. The linear differential operator of the equation is neither monotone nor coercive due to the presence of a convection term. The control appears only linearly, or even it can not appear in an explicit form in the objective functional. Under new assumptions, we prove Lipschitz stability of the optimal controls and associated states with respect to perturbations in the equation and the objective functional as well as with respect to the Tikhonov regularization parameter.

References in corpus (1)

• Stability in affine optimal control problems constrained by semilinear elliptic partial differential equations

Cited by in corpus (3)

• Stability analysis of the Navier-Stokes velocity tracking problem with bang-bang controls
• Stability and genericity of bang-bang controls in affine problems
• Solution stability of parabolic optimal control problems with fixed state-distribution of the controls