  We consider an initial value problem for a nonlinear parabolic equation with
memory under nonlinear nonlocal boundary condition. In this paper we study
classical solutions. We establish the existence of a local maximal solution. It
is shown that under some conditions a supersolution is not less than a
subsolution. We find conditions for the positiveness of solutions. As a
consequence of the positiveness of solutions and the comparison principle of
solutions, we prove the uniqueness theorem.
