Geodesic
Solution stability of parabolic optimal control problems with fixed state-distribution of the controls
Serdica Mathematical Journal, Tome 49 (2023) no. 1–3, pp. 155-186.

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The paper presents results about strong metric subregularity of the optimality mapping associated with the system of first order necessary optimality conditions for a problem of optimal control of a semilinear parabolic equation. The control has a predefined spacial distribution and only the magnitude at any time is a subject of choice. The obtained conditions for subregularity imply, in particular, sufficient optimality conditions that extend the known ones. The paper is complementary to a companion one by the same authors, in which a distributed control is considered.
Keywords: optimal control, parabolic PDE, stability with respect to perturbations, 49N60, 49K20, 35K58 
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Corella, Alberto Domínguez; Jork, Nicolai; Veliov, Vladimir. Solution stability of parabolic optimal control problems with fixed state-distribution of the controls. Serdica Mathematical Journal, Tome 49 (2023) no. 1–3, pp. 155-186. http://geodesic.mathdoc.fr/item/SMJ2_2023_49_1_3_a8/