Messoud Efendiev, Vitali Vougalter
On the necessary conditions for preserving the nonnegative cone: mixed diffusion
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ABSTRACT.  The article 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 arbitary 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.