A degenerate parabolic system for three-phase flows in porous media

Vladimir Shelukhin

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Qualitative study of nonlinear parabolic equations: an introduction.

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Higher integrability for weak solutions of higher order degenerate parabolic systems.

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Wojciech Zajączkowski (1996)

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Existence of weak solutions and an $L_{\infty}$ -estimate are shown for nonlinear nondegenerate parabolic systems with linear growth conditions with respect to the gradient. The $L_{\infty}$ -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.

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