Abstract. In this paper we give a characterization for the uniform exponential stability of evolution families $\{\Phi(t,t_0)\}_{t\geq t_0}$ on $\mathbb R_+$ that are not a priori required to be bounded, using the hypothesis that the pairs of function spaces $(L^1(X),L^\infty (X))$ and $(\mathcal C_{00}(\mathbb R_+,X),\mathcal C(\mathbb R_+,X))$ are admissible to the evolution families.

DOI: 10.14232/actasm-012-562-2

AMS Subject Classification (1991): 34D05, 34D09

Keyword(s): evolution family, admissibility, uniform exponential stability, asymptotic property

Received August 21, 2012. (Registered under 62/2012.)