On the existence of periodic solutions of some nonlinear problems of thermal control

From the text (translated from the Russian): "We consider the heat equation with a boundary condition containing a control function. The control function is a solution of an ordinary differential equation whose right-hand side contains a nonlinear functional that models the hysteresis effect. The dependence of the functional on the mean temperature over the domain causes nonlocal effects. Such problems arise in the modeling of thermal control processes in chemical reactors and climate control systems. We study the solvability and periodicity of the solutions of the problem."