Uniqueness of the renormalized solutions to the Cauchy problem for an anisotropic parabolic equation

F. Kh. Mukminov

Ufa mathematical journal, Tome 8 (2016) no. 2, pp. 44-57

Résumé

We consider the Cauchy problem for a certain class of anisotropic parabolic second-order equations with double non-power nonlinearities. The equation contains an “inhomogeneity” in the form of a non-divergent term depending on the sought function and spatial variables. Non-linearities are characterized by $N$-functions, for which $Delta_2$-condition is not imposed. The uniqueness of renormalized solutions in Sobolev–Orlich spases is proved by the S. N. Kruzhkov method of doubling the variables.

Détail

Keywords: renormalized solution, non-power nonlinearities, $N$-functions, uniqueness of solution.
Mots-clés : anisotropic parabolic equation

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