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 Mat. Sb., 2014, Volume 205, Number 1, Pages 9–46 (Mi msb8243)

Solutions to higher-order anisotropic parabolic equations in unbounded domains

L. M. Kozhevnikova, A. A. Leont'ev

Sterlitamak branch of Bashkir State University

Abstract: The paper is devoted to a certain class of doubly nonlinear higher-order anisotropic parabolic equations. Using Galerkin approximations it is proved that the first mixed problem with homogeneous Dirichlet boundary condition has a strong solution in the cylinder $D=(0,\infty)\times\Omega$, where $\Omega\subset\mathbb R^n$, $n\geq 3$, is an unbounded domain. When the initial function has compact support the highest possible rate of decay of this solution as $t\to \infty$ is found. An upper estimate characterizing the decay of the solution is established, which is close to the lower estimate if the domain is sufficiently ‘narrow’. The same authors have previously obtained results of this type for second order anisotropic parabolic equations.
Bibliography: 29 titles.

Keywords: higher-order anisotropic equation, parabolic equation with double nonlinearity, existence of a solution, rate of decay of a solution.

 Funding Agency Grant Number Russian Foundation for Basic Research 13-01-00081-a

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8243

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English version:
Sbornik: Mathematics, 2014, 205:1, 7–44

Bibliographic databases:

UDC: 517.956.4
MSC: 35K35

Citation: L. M. Kozhevnikova, A. A. Leont'ev, “Solutions to higher-order anisotropic parabolic equations in unbounded domains”, Mat. Sb., 205:1 (2014), 9–46; Sb. Math., 205:1 (2014), 7–44

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb8243
• https://doi.org/10.4213/sm8243
• http://mi.mathnet.ru/eng/msb/v205/i1/p9

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. E. R. Andriyanova, “Estimates of decay rate for solution to parabolic equation with non-power nonlinearities”, Ufa Math. J., 6:2 (2014), 3–24
2. E. R. Andriyanova, F. Kh. Mukminov, “Existence of solution for parabolic equation with non-power nonlinearities”, Ufa Math. J., 6:4 (2014), 31–47
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
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