Dissipative Quasi-Stable Systems: Theory and Applications
Thursday, October 18, 2012 - 10:30am - 12:00pm
We discuss properties of a class of dissipative dynamical systems which display rather special long time dynamics. This class is referred to as quasi-stable systems. It turns out that this is quite large class of systems naturally occurs in nonlinear PDE models arising in wave dynamics, plasma physics, thermoelasticity of plates and gas/fluid-structure interaction models. The interest in this class of systems stems from the fact that quasi-stability inequality almost automatically implies number of desirable properties such as asymptotic smoothness, finite dimensionality of attractors, regularity of attractors, exponential attraction, etc. The notion of quasi-stability is rather natural from the point of view of long-time behavior. It pertains to decomposition of the flow into exponentially stable and compact part. This represents some sort of analogy with the splitting method, however, the decomposition refers to the difference of two trajectories, rather than a single trajectory.