THE UNIVERSITY OF ALABAMA IN HUNTSVILLE
DEPARTMENT OF MATHEMATICAL SCIENCES
UAH Karen Ames Memorial Lecture Series
Dr. Irena Lasiecka
Department of Mathematical Sciences, University of Memphis
"Mathematical Theory of Evolutions Arising in Flow Structure Interactions"
Abstract - An appearance of a flutter in oscillating structures is an endemic phenomenon. Most common causes are vibrations induced by the moving flow of a gas (air, liquid) which is interacting with the structure. Typical examples include: turbulent jets, vibrating bridges [Tacoma bridge], oscillating facial palate at the onset of apnea. In the case of an aircraft it may compromise its safety. The intensity of the flutter depends heavily on the speed of the flow (subsonic, transonic or supersonic regimes). Thus, reduction or attenuation of flutter is one of the key problems in aero elasticity with applications to a variety of fields including aerospace engineering, structural engineering, medicine and life sciences. Mathematical models describing this phenomenon involve strongly coupled systems of partial differential equations (Euler Equation and nonlinear plate equation) with interaction at the interface - which is the boundary surface of the structure. The analysis of the model leads to consideration of nonlocal PDE’s. This talk aims at providing a brief overview of recent developments in the area along with a presentation of some recent advances. More specifically the following general issues will be discussed :(1) qualitative properties of the resulting dynamical systems (existence, uniqueness and robustness of weak solutions), (2) asymptotic stability and associated long time behavior that includes the study of global attractors, (3) feedback control strategies aiming at the elimination or attenuation of the flutter. Since the properties of the flutter depend heavily on the speed of the flow (subsonic, transonic or supersonic), it is natural that the resulting mathematical theories will be very different in the subsonic and supersonic regimes. In fact, supersonic flows are known for depleting ellipticity from the corresponding static model. Thus, both wellposedness of finite energy solutions and longtime behavior of the model have been open questions in the literature. The results presented include: generation of a dynamical system associated with the model. Existence of global and finite dimensional attracting sets for the elastic structure in the absence of mechanical dissipation. Strong convergence to multiple equilibria for the subsonic models will be also discussed.
Refreshments will be served at 2:30 p.m. in the Math Office (SST 258A).
About Prof. Irena Lasiecka - Prof. Irena Lasiecka is currently a Distinguished University Professor of mathematics and Chair of the Department of Mathematical Sciences at the University of Memphis. Prior to her current appointment, she was a Commonwealth Professor of Mathematics at the University of Virginia. Prof. Lasiecka is co-editor-in-chief and associate editor of numerous mathematical journals. She is a Fellow of the AMS (American Mathematical Society) since 2015 for her “contributions to control theory of partial differential equations, mentorship, and service to professional societies”, IEEE Fellow since 2005 and became SIAM Fellow in 2019. She was awarded 2011 SIAM Reid Prize for her “contributions in differential equations and control“. Her research areas include partial differential equations, Control theory, Optimization theory, Calculus of variations, and Boundary stabilization. Prof. Lasiecka is an ISI Highly cited author with over 14,000 citations on Google Scholar and over 6500 citations on MathScinet. She authored over 10 books-monographs and over 380 research papers. Her research has continuously been supported by several agencies including The National Science Foundation (NSF), Air Force, U.S. Army, NATO, and NASA. Prof. Lasiecka is a frequent invited plenary speaker at the main conferences organized by SIAM, AMS (American Mathematical Society), IFIP (International Federation of Information Processing), IEEE, AIMS (American Institute of Mathematical Sciences), etc. She directed 28 PhD students and mentored 16 Postdoctoral students all of whom have successful professional careers in Academia, Industry, or in Research Labs.
