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Ufimsk. Mat. Zh., 2011, Volume 3, Issue 4, Pages 64–85 (Mi ufa119)  

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

Estimates of solutions of an anisotropic doubly nonlinear parabolic equation

L. M. Kozhevnikova, A. A. Leontiev

Sterlitamak State Pedagogical Academy, Sterlitamak, Russia

Abstract: The first mixed problem with the Dirihlet homogeneous boundary-value condition and a finite initial function is considered for a certain class of second-order anisotropic doubly nonlinear parabolic equations in a cylindrical domain $D=(0,\infty)\times\Omega$. Upper estimates characterizing the dependence of the decay rate of the solution to the problem on geometry of an unbounded domain $\Omega\subset\mathbb R_n$, $n\geq3$, are established when $t\to\infty$. Existence of strong solutions is proved by the method of Galerkin's approximations. The method of their construction for the modelling isotropic equation has been earlier offered by F. Kh. Mukminov, E. R. Andriyanova. The estimate of the admissible decay rate of the solution on an unbounded domain has been obtained on the basis of Galerkin's approximations. It proves the accuracy of the upper estimate.

Keywords: anisotropic equation, doubly nonlinear parabolic equations, existence of strong solution, decay rate of solution.

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Document Type: Article
UDC: 517.946
Received: 15.07.2011

Citation: L. M. Kozhevnikova, A. A. Leontiev, “Estimates of solutions of an anisotropic doubly nonlinear parabolic equation”, Ufimsk. Mat. Zh., 3:4 (2011), 64–85

Citation in format AMSBIB
\Bibitem{KozLeo11}
\by L.~M.~Kozhevnikova, A.~A.~Leontiev
\paper Estimates of solutions of an anisotropic doubly nonlinear parabolic equation
\jour Ufimsk. Mat. Zh.
\yr 2011
\vol 3
\issue 4
\pages 64--85
\mathnet{http://mi.mathnet.ru/ufa119}
\zmath{https://zbmath.org/?q=an:1249.35174}


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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. L. M. Kozhevnikova, A. A. Leontev, “Resheniya anizotropnykh parabolicheskikh uravnenii s dvoinoi nelineinostyu v neogranichennykh oblastyakh”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(30) (2013), 82–89  mathnet  crossref
    2. L. M. Kozhevnikova, A. A. Leontiev, “Decay of solution of anisotropic doubly nonlinear parabolic equation in unbounded domains”, Ufa Math. J., 5:1 (2013), 63–82  mathnet  crossref  mathscinet  elib
    3. È. R. Andriyanova, F. Kh. Mukminov, “Stabilization of the solution of a doubly nonlinear parabolic equation”, Sb. Math., 204:9 (2013), 1239–1263  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. L. M. Kozhevnikova, A. A. Leont'ev, “Solutions to higher-order anisotropic parabolic equations in unbounded domains”, Sb. Math., 205:1 (2014), 7–44  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. E. R. Andriyanova, “Estimates of decay rate for solution to parabolic equation with non-power nonlinearities”, Ufa Math. J., 6:2 (2014), 3–24  mathnet  crossref  elib
    6. L. M. Kozhevnikova, A. A. Khadzhi, “Boundedness of solutions to anisotropic second order elliptic equations in unbounded domains”, Ufa Math. J., 6:2 (2014), 66–76  mathnet  crossref  elib
    7. A. A. Khadzhi, “Ubyvanie reshenii anizotropnykh ellipticheskikh uravnenii s mladshimi chlenami v neogranichennykh oblastyakh”, Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. Ser. Matematika. Fizika, 34:5 (2014), 78–87  elib
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