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Ufimsk. Mat. Zh., 2011, Volume 3, Issue 3, Pages 3–14 (Mi ufa99)  

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

The lower estimate of decay rate of solutions for doubly nonlinear parabolic equations

E. R. Andriyanova, F. Kh. Mukminov

Ufa State Aviation Technical University, Ufa, Russia

Abstract: Existence of strong solution to doubly nonlinear parabolic equation is established on unbounded domains by the method of Galerkin's approximations. In early publications existence was proved usually on bounded domains by approximating the evolution part of the equation by finite differences. Usage of Galerkin's approximations makes it possible to prove the second integral identity. On the basis of the identity, the bottom estimate of decay rate of the solution norm is proved on bounded domains. Similar estimates for quasilinear parabolic equations were established earlier by Tedeev A. F. and Alikakos N., Rostmanian R.

Keywords: doubly nonlinear parabolic equation, decay rate of solution, bottom estimates, existence of strong solution.

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Document Type: Article
UDC: 517.946
Received: 03.06.2011

Citation: E. R. Andriyanova, F. Kh. Mukminov, “The lower estimate of decay rate of solutions for doubly nonlinear parabolic equations”, Ufimsk. Mat. Zh., 3:3 (2011), 3–14

Citation in format AMSBIB
\Bibitem{AndMuk11}
\by E.~R.~Andriyanova, F.~Kh.~Mukminov
\paper The lower estimate of decay rate of solutions for doubly nonlinear parabolic equations
\jour Ufimsk. Mat. Zh.
\yr 2011
\vol 3
\issue 3
\pages 3--14
\mathnet{http://mi.mathnet.ru/ufa99}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3428997}
\zmath{https://zbmath.org/?q=an:1249.35144}


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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, “Otsenki resheniya anizotropnogo parabolicheskogo uravneniya s dvoinoi nelineinostyu”, Ufimsk. matem. zhurn., 3:4 (2011), 64–85  mathnet  zmath
    2. 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
    3. 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
    4. 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
    5. 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
    6. 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
    7. E. R. Andriyanova, F. Kh. Mukminov, “Existence of solution for parabolic equation with non-power nonlinearities”, Ufa Math. J., 6:4 (2014), 31–47  mathnet  crossref
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