Generalized solvability and optimization of a parabolic system with a discontinuous solution.

*(English)*Zbl 1113.35025The paper considers optimal control problems governed by a linear parabolic equation with specificic jump conditions on the interface between two parts of the spatial reference domain. The author introduces a specific notion of a generalized solution for the state equation and gives some sufficient conditions for the existence of such solutions. These results are applied to cases with the right hand side of the equation as a control, among them the case with the pulse control, and some properties of differentiability of the cost functional with respect to the control and existence of an optimal control are established.

Reviewer: Uldis Raitums (Riga)

##### MSC:

35B37 | PDE in connection with control problems (MSC2000) |

49J20 | Existence theories for optimal control problems involving partial differential equations |

35K10 | Second-order parabolic equations |

##### Keywords:

linear equation; parabolic equation; discontinuous solution; transmission problem; solvability; optimization; distribution; pulse control
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\textit{D. Nomirovskii}, J. Differ. Equations 233, No. 1, 1--21 (2007; Zbl 1113.35025)

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