We study the problem of optimal control over the processes described by the heat equation and a system of ordinary differential equations. For the problem of optimal control, we prove the existence and uniqueness of solutions, establish sufficient conditions for the Fréchet differentiability of the purpose functional, deduce the expression for its gradient, and obtain necessary conditions of optimality in the form of an integral maximum principle.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 7, pp. 962–972, July, 2015.
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Teimurov, R.A. Optimal Control over Moving Sources in the Heat Equation. Ukr Math J 67, 1091–1102 (2015). https://doi.org/10.1007/s11253-015-1136-7
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DOI: https://doi.org/10.1007/s11253-015-1136-7