Total approximation method for an equation describing droplet breakup and freezing in convective clouds

A locally one-dimensional scheme for a general parabolic equation in a $p$ -dimensional parallelepiped is considered. A special nonlocal integral source is added to the considered equation to describe droplet breakup and freezing in convective clouds. An a priori estimate for the solution of the locally one-dimensional scheme is obtained, and its convergence is proved.