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Optimal control over moving sources in the heat equation. (English. Russian original) Zbl 1378.49021

Ukr. Math. J. 67, No. 7, 1091-1102 (2015); translation from Ukr. Mat. Zh. 67, No. 7, 962-972 (2015).
Summary: 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.

MSC:

49K20 Optimality conditions for problems involving partial differential equations
49M25 Discrete approximations in optimal control
49K15 Optimality conditions for problems involving ordinary differential equations
49J50 Fréchet and Gateaux differentiability in optimization
35K05 Heat equation
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