On polynomial stability for skew-evolution semiflows on Banach spaces

Codruta Stoica (1)

1 IMB - Institut de Mathématiques de Bordeaux

Many of the processes that arise in engineering, physics or economics can be described by mathematical models that imply nonlinear evolution equations. Of great interest is, as we emphasize in this paper, to study the study the solutions of differential equations using an original concept, the skew-evolution semiflows, which generalize the classic notions of evolution operators and skew-product semiflows. The techniques from the domain of nonautonomous equations in infinite dimensions with unbounded coefficients are extended for the study of the above categories. The main concern of this paper is to give definitions, examples, connections and characterizations for various concepts for the asymptotic properties of stability of solutions for evolution equations in a nonuniform setting.

Mots clés: Barreira-Valls exponential stability; polynomial stability; skew-evolution semiflow; exponential stability

Domaines: Analyse classique [math.CA]

Codruta Stoica. On polynomial stability for skew-evolution semiflows on Banach spaces. 2010. ⟨hal-00641559⟩