Asymptotic stability of nonlinear hyperbolic equations

Abstract

The main subject of this project is the study of the long-time behavior of solutions of certain hyperbolic evolution equations by means of the theory of infinite dimensional dynamical systems. In view of the applicability of such differential equations in engineering and technology, this project integrates mathematical modeling and mathematical analysis of several real world problems. It also contributes to the development of new methods for the control and stabilization of dissipative systems. Specially for problems of vibrations of plates, thermo and visco-elastic systems, and modeling of special materials. To these problems, one discuses the global solvability, asymptotic stability and existence of attractors. The present project also integrates some doctoral dissertation projects. (AU)