In this paper, we characterize the stabilization of some delay systems. The proof of the main result uses the method introduced in Ammari and Tucsnak (ESAIM COCV 6:361-386, 2001) where the exponential stability for the closed loop problem is reduced to an observability estimate for the corresponding uncontrolled system combined with a boundedness property of the transfer function of the associated open loop system.

In this paper, we are interested in the wellposedness of inhomogeneous nonautonomous boundary Cauchy problems. We prove variation of constants formulas and Dyson-Phillips series which will allow us to study the asymptotic behaviour of the solutions to these problems. 1991 Mathematics Subject Classification: 34B05, 35B15, 35B20, 35B35.8 > < > : ð1:1Þwhere J :¼ R or R þ , A max ðtÞ is an unbounded operator on a Banach space X endowed with a maximal domain DðA max ðtÞÞ, and LðtÞ : DðA max ðtÞÞ ! qX , FðtÞ : X ! qX , t A J, with qX is a 'boundary space'. These abstract problems model natural phenomena such as population equations, retarded di¤erential (di¤erence) equations and boundary control problems. In the autonomous case, their study was started by Greiner [21,22,23] using the perturbation of the domains of semigroups, and Desch-This work is finished while the second author was visiting Tü bingen University. He would like to thank Rainer Nagel and Roland Schnaubelt for many useful discussions and comments, and he is grateful for the financial support of the Alexander von Humboldt Foundation. The third author acknowledges the partial support of ''Centre International de Systèmes Dynamiques (CISD)'' at Caddi Ayyad University Marrakesh. Brought to you by | Tulane University Authenticated Download Date | 1/4/15 12:21 AM Brought to you by | Tulane University Authenticated Download Date | 1/4/15 12:21 AM Brought to you by | Tulane University Authenticated Download Date | 1/4/15 12:21 AM

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The paper is concerned with the existence of almost periodic solutions to the so-called semilinear thermoelastic plate systems. For that, the strategy consists of seeing these systems as a particular case of the semilinear parabolic evolution equationswhere A(t) for t ∈ R is a family of sectorial linear operators on a Banach space X satisfying the so-called Acquistapace-Terreni conditions, and f is a function defined on a real interpolation space X α for α ∈ (0, 1). Under some reasonable assumptions it will be shown that ( * ) has a unique almost periodic solution. We then make use of the previous result to obtain the existence and uniqueness of an almost periodic solution to the thermoelastic plate systems.

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