Automatic control problems for reaction-diffusion systems

A class of nonlinear reaction-diffusion systems is considered. We formulate some automatic control problems based on feedback devices located on the boundary. Two different types of devices are analyzed: relay switch and Preisach hysteresis operator. The resulting models lead to a nonlinear integrodifferential parabolic system with nonlinear and nonlocal boundary conditions. We prove global existence and uniqueness of solutions in both the cases considered