Article

    Ufa Mathematical Journal
    Volume 8, Number 2, pp. 44-57

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


    Mukminov F.Kh.

    DOI:10.13108/2016-8-2-44

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    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.