  This paper deals with a parabolic partial differential equation that includes
a non-linear nonlocal in time term. This term is the product of a so-called
interaction potential and the solution of the problem. The interaction
potential depends on a weighted integral of the solution over the entire time
interval, where the problem is considered, and satisfies fairly general
conditions. Namely, it is assumed to be a continuous bounded from below
function that can behave arbitrarily at infinity. This fact implies that the
interaction term is not a lower order term in the equation. The weak
solvability of the initial boundary value problem for this equation is proven.
The proof does not use any continuity properties of the solution with respect
to time and is based on the energy estimate only.
