We consider the coupled PDEs/ODEs system modelling the motion of a solid in a viscous heat conducting gas. We first develop a systematic approach to obtain local well-posedness and asymptotic stability results. We next show that in the one dimensional case (the piston problem) some of our results are global. We also discuss the so called "adiabatic piston" problem, which is still of big interest in statistical physics. Finally, we show that for a simplified problem we obtain finite time controllability.
Marius Tucsnak received the Master degree in Mathematics from the University of Bucharest, Romania, in 1985 and the Ph.D. degree in Mathematics from the University of Orléans, France, in 1992. He has been working at Institute of Mathematics of the Romanian Academy (Bucharest), University of Versailles and University of Lorraine, France. He is currently with University of Bordeaux, France. In 2013 he has been designed senior member of Institut Universitaire de France. His research interests are control of systems governed by partial differential equations (such as the wave, Schrödinger or nonlinear plate equations), analysis and control of fluid–structure interactions. He is a coauthor (with George Weiss) of the book Observation and Control for Operator Semigroups (Birkhauser, 2009) and of 80 research articles published in major international journals.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai