  A system of a parabolic partial differential equation coupled with ordinary
differential inclusions that arises from a closed-loop control problem for a
thermodynamic process governed by the Allen-Cahn diffusion reaction model is
studied. A feedback law for the closed-loop control is proposed and implemented
in the case of a finite number of control devices located inside the process
domain basing on the process dynamics observed at a finite number of
measurement points. The existence of solutions to the discussed system of
differential equations is proved with the use of a generalization of the
Kakutani fixed point theorem.
