Abstract

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.

中文翻译：

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对流云中液滴破裂和冻结的方程的总逼近方法

摘要

考虑在（（p））维平行六面体中，一般抛物方程的局部一维格式。一个特殊的非局部积分源被添加到所考虑的方程中，以描述对流云中的液滴破裂和冻结。获得了局部一维格式解的先验估计，并证明了其收敛性。