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This article is cited in 7 scientific papers (total in 7 papers)
Decay of solution of anisotropic doubly nonlinear parabolic equation in unbounded domains
L. M. Kozhevnikova, A. A. Leontiev Sterlitamak State Pedagogical Academy
Abstract:
This work is devoted to a class of parabolic equations with double nonlinearity whose representative is a model equation $$(|u|^{k-2}u)_t=\sum_{\alpha=1}^n(|u_{x_{\alpha}} |^{p_{\alpha}-2}u_{x_{\alpha}})_{x_\alpha},\quad p_n\geq \ldots \geq p_1>k,\quad k\in(1,2).$$ For the solution of the first mixed problem in a cylindrical domain $ D=(0,\infty)$ $\times\Omega, \;$ ${\Omega\subset \mathbb{R}_n,}$ $\;n\geq 2$ with homogeneous Dirichlet boundary condition and compactly supported initial function precise estimates the rate of decay as $t\rightarrow\infty$ are established. Earlier these results were obtained by the authors for $k\geq 2$. The case $k\in(1,2)$ differs by the method of constructing Galerkin's approximations that for an isotropic model equation was proposed by E. R. Andriyanova and F. Kh. Mukminov.
Keywords:
anisotropic equation, doubly nonlinear parabolic equations, existence of strong solution, decay rate of solution.
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English version:
Ufa Mathematical Journal, 2013, 5:1, 63–82 (PDF, 448 kB); https://doi.org/10.13108/2013-5-1-63
Bibliographic databases:
UDC:
517.946 Received: 23.12.2011
Citation:
L. M. Kozhevnikova, A. A. Leontiev, “Decay of solution of anisotropic doubly nonlinear parabolic equation in unbounded domains”, Ufimsk. Mat. Zh., 5:1 (2013), 63–82; Ufa Math. J., 5:1 (2013), 63–82
Citation in format AMSBIB
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\jour Ufimsk. Mat. Zh.
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\pages 63--82
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\jour Ufa Math. J.
\yr 2013
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\crossref{https://doi.org/10.13108/2013-5-1-63}
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This publication is cited in the following articles:
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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
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L. M. Kozhevnikova, A. A. Leont'ev, “Solutions to higher-order anisotropic parabolic equations in unbounded domains”, Sb. Math., 205:1 (2014), 7–44
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E. R. Andriyanova, “Estimates of decay rate for solution to parabolic equation with non-power nonlinearities”, Ufa Math. J., 6:2 (2014), 3–24
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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
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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
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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
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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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