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 equationsequation(*)x′(t)=A(t)x(t)+f(t,x(t)),t∈R, where A(t)A(t) for t∈Rt∈R is a family of sectorial linear operators on a Banach space XX satisfying the so-called Acquistapace–Terreni conditions, and f   is a function defined on a real interpolation space XαXα for α∈(0,1)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.