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Ufimsk. Mat. Zh., 2014, Volume 6, Issue 2, Pages 3–25 (Mi ufa239)  

This article is cited in 5 scientific papers (total in 5 papers)

Estimates of decay rate for solution to parabolic equation with non-power nonlinearities

E. R. Andriyanova

Ufa State Aviation Technical University, Ufa, Russia

Abstract: We study the Dirichlet mixed problem for a class parabolic equation with double non-power nonlinearities in cylindrical domain $D=(t>0)\times\Omega$. By the Galerkin approximations method suggested by Mukminov F. Kh. for a parabolic equation with double nonlinearities we prove the existence of strong solutions in Sobolev–Orlicz space. The maximum principle as well as upper and lower estimates characterizing powerlike decay of solution as $t\to\infty$ in bounded and unbounded domains $\Omega\subset R_n$ are established.

Keywords: parabolic equation, $N$-functions, existence of solution, estimate of decay rate of solution, Sobolev–Orlicz spaces.

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English version:
Ufa Mathematical Journal, 2014, 6:2, 3–24 (PDF, 473 kB); https://doi.org/10.13108/2014-6-2-3

Document Type: Article
UDC: 517.946
MSC: 35D05, 35B50, 35B45, 35K55
Received: 14.11.2013

Citation: E. R. Andriyanova, “Estimates of decay rate for solution to parabolic equation with non-power nonlinearities”, Ufimsk. Mat. Zh., 6:2 (2014), 3–25; Ufa Math. J., 6:2 (2014), 3–24

Citation in format AMSBIB
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\by E.~R.~Andriyanova
\paper Estimates of decay rate for solution to parabolic equation with non-power nonlinearities
\jour Ufimsk. Mat. Zh.
\yr 2014
\vol 6
\issue 2
\pages 3--25
\mathnet{http://mi.mathnet.ru/ufa239}
\elib{http://elibrary.ru/item.asp?id=21596971}
\transl
\jour Ufa Math. J.
\yr 2014
\vol 6
\issue 2
\pages 3--24
\crossref{https://doi.org/10.13108/2014-6-2-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928186140}


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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. 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
    2. L. M. Kozhevnikova, A. A. Khadzhi, “O resheniyakh ellipticheskikh uravnenii s nestepennymi nelineinostyami v neogranichennykh oblastyakh”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:1 (2015), 44–62  mathnet  crossref  zmath  elib
    3. È. R. Andriyanova, F. Kh. Mukminov, “Existence and qualitative properties of a solution of the first mixed problem for a parabolic equation with non-power-law double nonlinearity”, Sb. Math., 207:1 (2016), 1–40  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. F. Kh. Mukminov, “Uniqueness of the renormalized solutions to the Cauchy problem for an anisotropic parabolic equation”, Ufa Math. J., 8:2 (2016), 44–57  mathnet  crossref  isi  elib
    5. F. Kh. Mukminov, “Uniqueness of the renormalized solution of an elliptic-parabolic problem in anisotropic Sobolev-Orlicz spaces”, Sb. Math., 208:8 (2017), 1187–1206  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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