Geodesic
On a~weak (algebraic) extremum principle for a~second-order parabolic system
Izvestiya. Mathematics , Tome 61 (1997) no. 5, pp. 933-959.

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The notion of a weak “algebraic” extremum principle (WAEP) is introduced for second-order parabolic systems. It is based on the representation of the (coefficient) matrix of the system as a sum of matrices that are similar to diagonal matrices and nilpotent matrices, and on the reduction of the system to a single equation. The validity of the WAEP is proved for a rather broad class of second-order parabolic systems with “full mixing”. The WAEP is applied to prove the uniqueness of the solution of the first boundary-value problem for the parabolic systems in question. 
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L. A. Kamynin; B. N. Khimchenko. On a~weak (algebraic) extremum principle for a~second-order parabolic system. Izvestiya. Mathematics , Tome 61 (1997) no. 5, pp. 933-959. http://geodesic.mathdoc.fr/item/IM2_1997_61_5_a1/

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