Abstract
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.
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