Parabolic equations with hysteresis
Title: Parabolic equations with hysteresis
Speaker: Sergey Tikhomirov
From: St. Petersburg University, Russia
Time: April 10th 10:10-12:10
12th 11:15-12:15 14:00-15:00
13th 11:15-12:15 14:00-15:00
Abstract: Hysteresis operator naturally appears in control theory and as a mechanism of self-organisation. The main features of systems with hysteresis are the dependence of the output on the prehistory of the input, rate independence, and nonsmoothness. We consider various parabolic problems with hysteresis.
We start with a simple thermocontrol problem, where only one hysteretic unit is presented and study properties of their periodic solutions. The main part of the course is devoted to systems describing self-organisation mechanisms, where one observes uncountably many hysteretic units. We discuss relations of the problem to the free boundary problems and pattern formation.