Existence of weak solutions and an -estimate are shown for nonlinear nondegenerate parabolic systems with linear growth conditions with respect to the gradient. The -estimate is proved for equations with coefficients continuous with respect to x and t in the general main part, and for diagonal systems with coefficients satisfying the Carathéodory condition.
@article{bwmeta1.element.bwnjournal-article-bcpv33z1p491bwm,
author = {Zaj\k aczkowski, Wojciech},
title = {$L\_$\infty$$-estimates for solutions of nonlinear parabolic systems with gradient linear growth},
journal = {Banach Center Publications},
volume = {37},
year = {1996},
pages = {491-501},
zbl = {0856.35069},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv33z1p491bwm}
}
Zajączkowski, Wojciech. $L_∞$-estimates for solutions of nonlinear parabolic systems with gradient linear growth. Banach Center Publications, Tome 37 (1996) pp. 491-501. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv33z1p491bwm/
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