On the maximum-minimum principle for advection-diffusion equations

Abstract

The air pollution transport model is generally solved with the so-called operator splitting technique. The original problem is split into several subproblems and the solution of the model is obtained by solving the subproblems cyclically. In this paper, we analyze the advection, diffusion and emission subproblems. These subproblems have to possess certain qualitative properties that follow from physical considerations: nonnegativity preservation, maximumminimum principle and maximum norm contractivity. We show that these properties are valid for the subproblems, and we shad light on their relations.