In this paper, we give a characterization (optimality system) of a quadratic optimal control for an ill-posed wave equation without using the extra hypothesis of Slater (ie. 𝑼𝒂𝒅 set of admissible controls has a non-empty interior). By using a parabolic regularization we get a missing data problem where we associate a no-regret control to obtain a singular optimality system, then we pass to limit and by a corrector of order zero we complete the information.
عبدالحق حفظ الله | Abdelhak Hafdallah | 5258