- 18-78 Messoud Efendiev, Vitali Vougalter
- On the necessary conditions for preserving the nonnegative cone: mixed diffusion
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Jul 13, 18
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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.
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