Geodesic
An a priori estimate for solutions of some quasilinear parabolic systems.~II
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (1967), pp. 94-99

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In this paper the first boundary value problem for systems of type (I) is studied. Under some conditions on $\Phi$, $\Psi$ an apriori estimate for $|u|$ is established; in case when $\Psi=|u|^2$ from such an estimate it follows that the solution exists in the large. 
@article{VMUMM_1967_6_a9,
     author = {T. D. Ventsel'},
     title = {An a priori estimate for solutions of some quasilinear parabolic {systems.~II}},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {94--99},
     publisher = {mathdoc},
     number = {6},
     year = {1967},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1967_6_a9/}
}
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T. D. Ventsel'. An a priori estimate for solutions of some quasilinear parabolic systems.~II. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (1967), pp. 94-99. http://geodesic.mathdoc.fr/item/VMUMM_1967_6_a9/