Asymptotic stability of infinite-dimensional nonautonomous dynamical systems (Q2873822)

This paper investigates and surveys the concept of asymptotic stability for various nonautonomous evolutionary equations. The latter are formulated as abstract skew-product flows by means of the well-known Bebutov construction. In particular, the concepts of uniform stability, (eventual) uniform attraction, uniform asymptotic stability and global asymptotic stability are investigated and related. A particular focus is on almost periodic time dependence.NEWLINENEWLINEThe results are illustrated using ordinary differential equations, difference equations, functional differential equations (with finite delay, as well as of neutral type) and semilinear parabolic equations.