Title: Parabolic equations with hysteresis

Speaker: Sergey Tikhomirov

From: St. Petersburg University, Russia

Time: April 10^th 10:10-12:10

11^th  9:00-11:00

12^th  11:15-12:15  14:00-15:00

13^th  11:15-12:15  14:00-15:00

Room: N204

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.