Abstract:
We consider the simplest mathematical model of the following problem.
On the part of the border of region $D\subset {\mathbb R}^{2}$ there is a heater having an adjustable temperature. It is required to find such a mode of operation of
the heater so 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.
Keywords:parabolic equation, boundary value problem, control problem, control parameter, first kind Volterra integral equation, Laplace transform.
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