Applied Mathematics Colloquium: Dr. Ozkan Ozer

Title: Introducing Novel PDE Models of Piezoelectric Devices and Investigating Related Controllability Scenarios

Abstract: In this talk, novel PDE models for single-layer and multi-layer piezoelectric beam systems will be introduced. These models mainly couple the longitudinal and/or transverse vibrations of layers with the electro-magnetism due to Maxwell's equations and/or thermal effects. Recent results on the distributed and boundary controllability with/without delay and memory terms in the models will be discussed and certain mathematical hurdles will be addressed. Even though some of these PDE models are known to be exactly observable, their approximations by known methods are not able to mimic this behavior with respect to the discretization parameter. Recent results on the application of direct/indirect Fourier filtering techniques and the issues due to the non-compact coupling among the system equations and different wave speeds through the layers will be discussed. Open problems will be addressed.