An integral boundary-value problem in a layer for a system of linear partial differential equations

Criteria for the well-posedness and strong well-posedness (smoothness properties of solutions in comparison with given functions) of a boundary-value problem in an infinite layer $\mathbb R^n\times[0,T]$ are obtained for an evolution linear system of partial differential equations. The problem is studied in classes of functions of finite smoothness and with polynomial growth. The boundary condition has an integral form and contains an arbitrary linear differential operator in the space variables. The dependence of the well-posedness of this problem on the thickness $T$ of the layer in question is studied.