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
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.
parabolic equation, $N$-functions, existence of solution, estimate of decay rate of solution, Sobolev–Orlicz spaces.
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Ufa Mathematical Journal, 2014, 6:2, 3–24 (PDF, 473 kB); https://doi.org/10.13108/2014-6-2-3
MSC: 35D05, 35B50, 35B45, 35K55
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
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\paper Estimates of decay rate for solution to parabolic equation with non-power nonlinearities
\jour Ufimsk. Mat. Zh.
\jour Ufa Math. J.
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E. R. Andriyanova, F. Kh. Mukminov, “Existence of solution for parabolic equation with non-power nonlinearities”, Ufa Math. J., 6:4 (2014), 31–47
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
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
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
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