ИСТИНА

We study the problem of control over temperature conditions in industrial hothouses. For a model based on a one-dimensional parabolic equation on a bounded interval with quadratic cost functional, we prove the existence and uniqueness of a control function from a prescribed set and study the structure of the set of accessible temperature functions. We prove the positivity principle to the parabolic boundary value problem and obtain the inequality for positive solutions. Also we prove some <<technological>> inequalities for the control function.