Boundary Control of the Heat Transfer Process in the Space

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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