Attractors for Delayed, Non-Rotational von Karman Plates with Applications to Flow-Structure Interactions Without any Damping

摘要

This paper is devoted to a long time behavior analysis associated with flowstructure interactions at subsonic and supersonic velocities. It turns out thatan ntrinsic component of that analysis is the study of attracting setscorresponding to von Karman plate equations with {\it delayed terms} and {\itwithout rotational} terms. The presence of delay terms in the dynamical systemleads to the loss of gradient structure while the absence of rotational termsin von Karman plates leads to the loss of compactness of the orbits. Both thesefeatures make the analysis of long time behavior rather subtle rendering theestablished tools in the theory of PDE dynamical systems not applicable. It isour goal to develop methodology that is capable of handling this class ofproblems.