Abstract
The paper studies the classical solvability of an inverse boundary value problem for a second order parabolic equation with nonlocal boundary conditions. For this purpose, first, the considered problem is reduced to an auxiliary equivalent problem in a certain sense. Then, using the Fourier method the auxiliary problem is presented as a system of integral equations. Further, by means of the contraction mappings principle the unique existence of the solution of the obtained system of integral equations is shown. At the end of investigation the existence and uniqueness theorem for the classical solution of the original inverse boundary value problem is proved based on the equivalence of these problems
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