Convergence to steady states in asymptotically autonomous semilinear evolution equations R. Chill 1 Abteilung Angewandte Analysis Universit¨atUlm 89069 Ulm, Germany chill@mathematik.uni-ulm.de and M.A. Jendoubi Universit´ e de Versailles Laboratoire de Math´ ematiques Appliqu´ ees Bˆ at. Fermat 45, avenue des Etats-Unis 78035 Versailles cedex, France jendoubi@math.uvsq.fr Abstract: We study the convergence to equilibrium of bounded solutions of the nonautonomous first order prob- lem ˙ u + Mu = g(t),t ∈ R + , and of the second order problem ¨ u +˙ u + Mu = g(t),t ∈ R + . Applications to diffusion, wave, Cahn-Hilliard and Kirchhoff- Carrier equations are described. 2000 Mathematics Subject Classification: Primary 34D05; Secondary 47D06, 34G10, 47B38 Keywords and phrases: convergence, analytic nonlinearity, nonautonomous, evolution equation. 1 The first author is supported by Deutscher Akademischer Austauschdienst (Stipendium im Rahmen des gemeinsamen Hochschulsonderprogramms III von Bund und L¨ andern ¨ uber den DAAD). This support is gratefully acknowledged 1