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High order nonlinear parabolic equations

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Abstract

The basic results and methods of the theory of high order nonlinear parabolic equations are described. In the first chapter boundary problems for quasilinear parabolic equations having divergent form are considered. In the second chapter nonlinear parabolic equations of general form are considered. Attention is mainly paid to methods of study of nonlinear parabolic problems. In particular, the methods of monotonicity and compactness, the method of a priori estimates, the functional-analytic method, etc. are described.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 37, pp. 89–166, 1990.

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Dubinskii, Y.A. High order nonlinear parabolic equations. J Math Sci 56, 2557–2607 (1991). https://doi.org/10.1007/BF01097353

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