Abstract
We consider the simplest mathematical model of the following problem. On a part of the border of a region D ⊂ ℝ2 there is a heater having the adjustable temperature. It is required to find a mode of operation of the heater such that the average temperature in a certain subregion of region D takes the specified value. The existence of the control parameter proved under certain restrictions on the values of the function defined by the integral constraint.
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Acknowledgments
The author is grateful to Academician Sh.A. Alimov for the attention to this work.
The author is grateful to the referee for constructive comments that contributed to the presentation improvement of the article results.
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Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 12, pp. 82–90.
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Fayazova, Z.K. Boundary Control of the Heat Transfer Process in the Space. Russ Math. 63, 71–79 (2019). https://doi.org/10.3103/S1066369X19120089
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DOI: https://doi.org/10.3103/S1066369X19120089