Parabolic problems with the Preisach hysteresis operator in boundary conditions

Parabolic initial boundary-value problems coupled (via the boundary condition) with ordinary differential equations whose right-hand side contains the Preisach hysteresis operator are considered. In particular, these problems model thermocontrol processes in chemical reactors, climate-control systems, biological cells, etc. For the Preisach operator with and without time delay, solvability, periodicity of solutions, and global B-attractors are studied.