  We consider the ill-posed Cauchy problem for the polyharmonic heat equation
on recovering a function, satisfying the equation $(\partial _t + (- \Delta)^m)
u=0$ in a cylindrical domain in the half-space ${\mathbb R}^n \times
[0,+\infty)$, where $n\geq 1$, $m\geq 1$ and $\Delta$ 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.
