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Mat. Sb., 2017, Volume 208, Number 8, Pages 106–125 (Mi msb8691)  

This article is cited in 7 scientific papers (total in 7 papers)

Uniqueness of the renormalized solution of an elliptic-parabolic problem in anisotropic Sobolev-Orlicz spaces

F. Kh. Mukminov

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

Abstract: We consider the first mixed problem for a class of anisotropic elliptic-parabolic equations with double variable nonlinearities in a cylindrical domain $(0,T)\times\Omega$. The domain $\Omega\subset\mathbb{R}^n$ can be unbounded. The uniqueness of the renormalized solution is proved using Kruzhkov's method of doubling the variable $t$. The same result is established for an equation with non-power law nonlinearities.
Bibliography: 24 titles.

Keywords: anisotropic parabolic equation, renormalized solution, variable nonlinearity, uniqueness of solution, $N$-function.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-07920-а
This research was supported by the Russian Foundation for Basic Research (grant no. 15-01-07920-a).


DOI: https://doi.org/10.4213/sm8691

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English version:
Sbornik: Mathematics, 2017, 208:8, 1187–1206

Bibliographic databases:

UDC: 517.954+517.956.45+517.958:531.72
MSC: Primary 35K55; Secondary 35A01, 35B05, 35B40, 35K20
Received: 04.03.2016 and 20.05.2016

Citation: F. Kh. Mukminov, “Uniqueness of the renormalized solution of an elliptic-parabolic problem in anisotropic Sobolev-Orlicz spaces”, Mat. Sb., 208:8 (2017), 106–125; Sb. Math., 208:8 (2017), 1187–1206

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kozhevnikova L.M., “On Solutions of Anisotropic Elliptic Equations With Variable Exponent and Measure Data”, Complex Var. Elliptic Equ.  crossref  isi
    2. V. F. Vildanova, F. Kh. Mukminov, “Suschestvovanie slabogo resheniya integro-differentsialnogo uravneniya agregatsii”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 63, no. 4, Rossiiskii universitet druzhby narodov, M., 2017, 557–572  mathnet  crossref
    3. 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
    4. F. Kh. Mukminov, “Existence of a renormalized solution to an anisotropic parabolic problem with variable nonlinearity exponents”, Sb. Math., 209:5 (2018), 714–738  mathnet  crossref  crossref  adsnasa  isi  elib
    5. V. F. Vil'danova, “On uniqueness of weak solution to mixed problem for integro-differential aggregation equation”, Ufa Math. J., 10:4 (2018), 40–49  mathnet  crossref  isi
    6. L. M. Kozhevnikova, “Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents”, Sb. Math., 210:3 (2019), 417–446  mathnet  crossref  crossref  elib
    7. Abercji A., Bennouna J., Elmassoudi M., Hammoumi M., “Existence and Uniqueness of a Renormalized Solution of Parabolic Problems in Orlicz Spaces”, Mon.heft. Math., 189:2 (2019), 195–219  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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