Almost periodic solutions to some semilinear non-autonomous thermoelastic plate equations

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 equations X '(t)=A(t)x(t)+f(t.x(t)), t is an element of R, (*) where A(t) for t is an element of 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 alpha for alpha is an element of (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. (C) 2008 Elsevier Inc. All rights reserved.