Existence of asymptotically almost automorphic solutions for a third order differential equation

Abstract

This paper deals with results on existence of asymptotically almost automorphic solutions for a third order in time abstract differential equation which model, on one side, high intensity ultrasound in acoustic wave propagation, while on the other side, vibrations of flexible structures possessing internal material damping. We established the asymptotically almost automorphy of the output solution subject to the asymptotically almost automorphy of the input disturbance.

Keywords

• third order differential equation
• asymptotically almost automorphic function
• regularized families of bounded operators