We consider the problem of optimal control formed by a parabolic nonlinear equation with rapidly oscillating coefficients, an additive control function, and a coercive cost functional. It is proved that the optimal value of the perturbed problem is close to the optimal value for the corresponding problem with averaged coefficients.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 7, pp. 973–979, July, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i7.7016.
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Kapustyan, O.V., Stanzhytskyi, O.M. & Fartushny, I.D. Averaging Method in the Problem of Optimal control for a Perturbed Parabolic Equation. Ukr Math J 74, 1113–1120 (2022). https://doi.org/10.1007/s11253-022-02123-0
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DOI: https://doi.org/10.1007/s11253-022-02123-0