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Ufimsk. Mat. Zh., 2016, Volume 8, Issue 2, Pages 44–58 (Mi ufa344)  

This article is cited in 1 scientific paper (total in 1 paper)

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

F. Kh. Mukminov

Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa

Abstract: 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.

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

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00081-a


Full text: PDF file (593 kB)
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English version:
Ufa Mathematical Journal, 2016, 8:2, 44–57 (PDF, 210 kB); https://doi.org/10.13108/2016-8-2-44

Bibliographic databases:

UDC: 517.954+517.956.45+517.958:531.72
MSC: 35D05, 35K55, 35B50, 35B45, 35B05
Received: 06.02.2016

Citation: F. Kh. Mukminov, “Uniqueness of the renormalized solutions to the Cauchy problem for an anisotropic parabolic equation”, Ufimsk. Mat. Zh., 8:2 (2016), 44–58; Ufa Math. J., 8:2 (2016), 44–57

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. F. Vil'danova, “Existence and uniqueness of a weak solution of a nonlocal aggregation equation with degenerate diffusion of general form”, Sb. Math., 209:2 (2018), 206–221  mathnet  crossref  crossref  adsnasa  isi  elib
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