heat conduction equation, admissible control, initial-boundary value problem, integral equation, уравнение теплопроводности, допустимое управление, начально-краевая задача, интегральное уравнение, Science

The initial-boundary problem for the heat conduction equation inside a bounded domain is considered. It is supposed that on the boundary of this domain the heat exchange takes place according to Newton’s law. The control parameter is equal to the magnitude of output of hot air and is defined on a givenmpart of the boundary. Then we determined the dependence T(θ) on the parameters of the temperature process when θ is close to critical value.