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Ufimsk. Mat. Zh., 2014, Volume 6, Issue 4, Pages 32–49 (Mi ufa258)  
This article is cited in 2 scientific papers (total in 2 papers)

Existence of solution for parabolic equation with non-power nonlinearities

E. R. Andriyanovaa, F. Kh. Mukminovb

a Ufa State Aviation Technical University, Ufa, Russia
b Bashkir State University, Ufa, Russia

Abstract: We consider the first mixed problem for a class of parabolic equation with double non-exponential nonlinearities in a cylindrical domain $D=(t>0)\times\Omega$. By Galerkin's approximations we prove the existence of strong solutions in Sobolev–Orlich space.

Keywords: parabolic equation, $N$-functions, existence of solution, Sobolev–Orlich spaces.

Full text: PDF file (624 kB)
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English version:
Ufa Mathematical Journal, 2014, 6:4, 31–47 (PDF, 431 kB); https://doi.org/10.13108/2014-6-4-31

UDC: 517.946
MSC: 35D05, 35B50, 35B45, 35K55
Received: 23.09.2014

Citation: E. R. Andriyanova, F. Kh. Mukminov, “Existence of solution for parabolic equation with non-power nonlinearities”, Ufimsk. Mat. Zh., 6:4 (2014), 32–49; Ufa Math. J., 6:4 (2014), 31–47

Citation in format AMSBIB
\Bibitem{AndMuk14}
\by E.~R.~Andriyanova, F.~Kh.~Mukminov
\paper Existence of solution for parabolic equation with non-power nonlinearities
\jour Ufimsk. Mat. Zh.
\yr 2014
\vol 6
\issue 4
\pages 32--49
\mathnet{http://mi.mathnet.ru/ufa258}
\transl
\jour Ufa Math. J.
\yr 2014
\vol 6
\issue 4
\pages 31--47
\crossref{https://doi.org/10.13108/2014-6-4-31}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928238743}


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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. 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
    2. 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
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