Special Session 50: Evolution equations and inclusions with applications to control, mathematical modeling and mechanics
Contents
The aim of the talk is to discuss doubly nonlinear hyperbolic-parabolic parameter dependent control system.
It will be shown that the coupled system of Maxwell\/'s equation and a heat equation on finite time interval in
one space dimension involving a phase transition property and Joule\/'s heating effect can be written in such a way.
This results into two multivalued nonlinearities in the system. Using frequency domain conditions for the hyperbolic-parabolic control system we derive sufficient conditions for bifurcation on a finite time interval. As an important part of the proof we show the existence of a cocycle of our nonautonomous parameter dependent control system.