On the solution stability of parabolic optimal control problems

Abstract The paper investigates stability properties of solutions optimal control problems constrained by semilinear parabolic partial differential equations. Hölder or Lipschitz dependence the solution on perturbations are obtained for in which equation and objective functional affine with respect to control. may appear both nonlinearly depend state variables. main results based an extension recently introduced assumptions joint growth first second variation functional. is as a consequence more general result paper–the metric subregularity mapping associated system order necessary optimality conditions. This property also enables error estimates approximation methods. A estimate Tikhonov regularization parameter by-product.