Abstract
We consider a parabolic problem with discontinuous hysteresis onthe boundary, arising in modelling various thermal controlprocesses. By reducing the problem to an infinite dynamicalsystem, sufficient conditions for the existence and uniqueness ofa periodic solution are found. Global stability of the periodicsolution is proved.
Highlights
Hysteresis operators naturally arise in mathematical description of many physical processes [17, 29, 5]
We deal with parabolic problems containing a discontinuous hysteresis operator in the boundary condition
We develop a new approach to the study of periodicity and large-time behavior of solutions of thermocontrol problems with discontinuous hysteresis on the boundary
Summary
Hysteresis operators naturally arise in mathematical description of many physical processes [17, 29, 5]. This was done in [13], where a thermocontrol problem with the Preisach hysteresis operator in the boundary condition was considered and the existence of periodic solutions and global attractors were established.
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