Siberian Federal University

We consider the ill-posed Cauchy problem for the polyharmonic heat equation on recovering a function, satisfying the equation (@t+(-Δ)m)u = 0 in a cylindrical domain in the half-space Rnx[0;+1), where n > 1, m > 1 and Δ is the Laplace operator, via its values and the values of its normal derivatives up to order (2m - 1) on a given part of the lateral surface of the cylinder. We obtain a Uniqueness Theorem for the problem and a criterion of its solvability in terms of the real-analytic continuation of parabolic potentials, associated with the Cauchy data