Exponential Stability versus Polynomial Stability for Skew-Evolution Semiflows in Infinite Dimensional Spaces

Abstract

As the dynamical systems that model processes issued from engineering, economics or physics are extremely complex, of
great interest is to study the solutions of dierential equations by means of associated evolution families. In this paper we emphasize
some notions of asymptotic stability for skew-evolution semiflows on Banach spaces, such as exponential and polynomial
stability, in a nonuniform setting. Examples for every concept and connections between them are also presented, as well as some
characterizations.