Mathematics for various disciplines Quasilinear hyperbolic equations with hysteresis

2007-12-04 15:00 - 2007-12-04 16:00
Graduate School of Mathematical Sciences the University of Tokyo, Room #122
Pavel Krejci (Weierstrass Institute for Applied Analysis and Stochastics)
We consider a wave propagation problem in a rate independent elastoplastic material described by a counterclockwise convex hysteresis operator. Unlike in viscoelasticity, the speed of propagation is bounded above by the speed of the corresponding elastic waves. The smoothening dissipative effect is due to the convexity of the hysteresis branches. We present some recent results on the long time behavior of solutions under various boundary conditions, including the stability of time periodic solutions under periodic forcing.