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Wellposedness and asymptotic behaviour of nonautonomous linear evolution equations
 A. Lorenzi, B. Ruf (Eds.): “Evolution Equations, Semigroups and Functional Analysis,” Birkhäuser
, 2002
"... We review results on the existence and the long term behaviour of nonautonomous linear evolution equations. Emphasis is put on recent results on the asymptotic behaviour using a semigroup approach. ..."
Abstract

Cited by 6 (4 self)
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We review results on the existence and the long term behaviour of nonautonomous linear evolution equations. Emphasis is put on recent results on the asymptotic behaviour using a semigroup approach.
Almost Periodicity of Inhomogeneous Parabolic Evolution Equations
 Report No.8, Fachbereich Mathematik und Informatik, Universitat
, 2002
"... We show the (asymptotic) almost periodicity of the bounded solution to the parabolic evolution equation u (t) = A(t)u(t) +f(t) on R (on R+ ) assuming that the linear operators A(t) satisfy the `Acquistapace{Terreni' conditions, that the evolution family generated by A() has an exponential dichotom ..."
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Cited by 6 (1 self)
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We show the (asymptotic) almost periodicity of the bounded solution to the parabolic evolution equation u (t) = A(t)u(t) +f(t) on R (on R+ ) assuming that the linear operators A(t) satisfy the `Acquistapace{Terreni' conditions, that the evolution family generated by A() has an exponential dichotomy, and that R(!; A()) and f are (asymptotically) almost periodic. 1.
Parabolic Evolution Equations With Asymptotically Autonomous Delay
 Report No.2, Fachbereich Mathematik und Informatik, Universitat
, 2001
"... . We study retarded parabolic nonautonomous evolution equations whose coefficients converge as t ! 1 such that the autonomous problem in the limit has an exponential dichotomy. Then the nonautonomous problem inherits the exponential dichotomy and the solution of the inhomogeneous equation ten ..."
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Cited by 3 (3 self)
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. We study retarded parabolic nonautonomous evolution equations whose coefficients converge as t ! 1 such that the autonomous problem in the limit has an exponential dichotomy. Then the nonautonomous problem inherits the exponential dichotomy and the solution of the inhomogeneous equation tends to the stationary solution at infinity. We use a generalized characteristic equation to deduce the exponential dichotomy and new representation formulas for the solution of the inhomogeneous equation. 1. Introduction In the present paper we continue the investigation of the longterm behaviour of asymptotically autonomous evolution equations begun in [30]. There we studied the Cauchy problem u(t) = A(t)u(t) + f(t); t ? s 0; u(s) = x; (1.1) on a Banach space X assuming that the linear operators A(t), t 0, are sectorial of the same type and satisfy the `AcquistapaceTerreni' condition (see (P) below) and that there exists another sectorial operator A such that lim t!1 R(w; A(t...