2012/08/26 by Igor Čhuešhov, Irena Lasiecka, Chueshov, Igor +3
Engineering · Physics and Astronomy · #35L20 #35Q74 #74F10 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1208.5245
openalex publication_date 2012/08/26 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28
This paper is devoted to a long time behavior analysis associated with flow\nstructure interactions at subsonic and supersonic velocities. It turns out that\nan ntrinsic component of that analysis is the study of attracting sets\ncorresponding to von Karman plate equations with it delayed terms and it\nwithout rotational terms. The presence of delay terms in the dynamical system\nleads to the loss of gradient structure while the absence of rotational terms\nin von Karman plates leads to the loss of compactness of the orbits. Both these\nfeatures make the analysis of long time behavior rather subtle rendering the\nestablished tools in the theory of PDE dynamical systems not applicable. It is\nour goal to develop methodology that is capable of handling this class of\nproblems.\n