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)×ΩD=(t>0)×Ω. By Galerkin's approximations we prove the existence of strong solutions in Sobolev–Orlich space.
Keywords:
parabolic equation, NN-functions, existence of solution, Sobolev–Orlich spaces.
Citation:
E. R. Andriyanova, F. Kh. Mukminov, “Existence of solution for parabolic equation with non-power nonlinearities”, Ufa Math. J., 6:4 (2014), 31–47
\Bibitem{AndMuk14}
\by E.~R.~Andriyanova, F.~Kh.~Mukminov
\paper Existence of solution for parabolic equation with non-power nonlinearities
\jour Ufa Math. J.
\yr 2014
\vol 6
\issue 4
\pages 31--47
\mathnet{http://mi.mathnet.ru/eng/ufa258}
\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}
Linking options:
https://www.mathnet.ru/eng/ufa258
https://doi.org/10.13108/2014-6-4-31
https://www.mathnet.ru/eng/ufa/v6/i4/p32
This publication is cited in the following 2 articles:
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
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
Citation in format AMSBIB
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