On the Necessary Conditions for Preserving the Nonnegative Cone: Mixed Diffusion

Abstract

The chapter deals with the easily verifiable necessary condition of the preservation of the nonnegativity of the solutions of a system of parabolic equations in the case of the mixed diffusion when the standard Laplacian in the first m variables is added to the Laplace operator in the rest of the variables in a fractional power in the space of an arbitrary dimension. This necessary condition is crucial for the applied analysis community since it imposes the necessary form of the system of equations that must be treated mathematically.