Nonlocal two-point boundary-value problems in a layer with differential operators in the boundary condition

We obtain criteria of well-posedness and strong well-posedness (smoothing of solutions as compared with given functions) of boundary-value problems for linear partial differential evolution equations in an infinite layer. The boundary condition is nonlocal and gives a relation between the values of the unknown function and its derivatives with respect to spatial coordinates on shifts of connected components of the boundary of the layer inside the layer.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 8, pp. 1122–1128, August, 1995.