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

This article is cited in 3 scientific papers (total in 3 papers)

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


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

Full text: PDF file (806 kB)
References: PDF file   HTML file

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

Bibliographic databases:

Document Type: Article
UDC: 517.956.4
MSC: 35K35
Received: 28.04.2013 and 07.11.2013

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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    Citing articles on Google Scholar: Russian citations, English citations
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    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  mathnet  crossref  elib
    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  mathnet  crossref
    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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