Nonlocal boundary-value problem for parabolic equations

We study the problem for Shilov parabolic equations of arbitrary order with constant coefficients with conditions nonlocal in time and periodic in space variables. We establish conditions for the existence and uniqueness of a classical solution of the problem and prove metric theorems on lower bounds of small denominators appearing in the construction of a solution of the problem.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 12, pp. 1621–1626, December, 1994.The work was supported by the Foundation for Fundamental Studies of Ukrainian State Committee on Science and Technology.