Geodesic
Heat flow for a~class of quadratic functionals with nondiagonal principal matrix. Existence of a~smooth global solution
Algebra i analiz, Tome 30 (2018) no. 2, pp. 45-75.

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A class of quasilinear parabolic systems with nondiagonal principal matrices and strongly nonlinear additional terms is considered. The elliptic operator of the system has a variational structure. The existence of a global smooth solution is proved in the case of two spatial variables.
Keywords: parabolic systems, strong nonlinearity, global solvability. 
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A. A. Arkhipova. Heat flow for a~class of quadratic functionals with nondiagonal principal matrix. Existence of a~smooth global solution. Algebra i analiz, Tome 30 (2018) no. 2, pp. 45-75. http://geodesic.mathdoc.fr/item/AA_2018_30_2_a2/

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