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 ∈ R , where 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.