Abstract
When we construct mathematical or numerical models in order to solve a real-life problem, it is important to preserve the characteristic properties of the original process. The models have to possess the equivalents of these properties. Parabolic partial equations generally serve as the mathematical models of heat conduction or diffusion processes, where the most important properties are the monotonicity, the nonnegativity preservation and the maximum principles. In this paper, the validity of the equivalents of these qualitative properties are investigated for the second order linear partial differential operator. Conditions are given that guarantee the qualitative properties. On some examples we investigate these conditions.
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