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 Mat. Sb., 2013, Volume 204, Number 9, Pages 3–28 (Mi msb8184)

Stabilization of the solution of a doubly nonlinear parabolic equation

È. R. Andriyanovaa, F. Kh. Mukminovb

a Ufa State Aviation Technical University
b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa

Abstract: The method of Galerkin approximations is employed to prove the existence of a strong global (in time) solution of a doubly nonlinear parabolic equation in an unbounded domain. The second integral identity is established for Galerkin approximations, and passing to the limit in it an estimate for the decay rate of the norm of the solution from below is obtained. The estimates characterizing the decay rate of the solution as $x\to\infty$ obtained here are used to derive an upper bound for the decay rate of the solution with respect to time; the resulting estimate is pretty close to the lower one.
Bibliography: 17 titles.

Keywords: doubly nonlinear parabolic equation, rate of decay of the solution, lower estimate, existence of a strong global (in time) solution.

 Funding Agency Grant Number Russian Foundation for Basic Research 10-01-00118-a13-01-00081-à

DOI: https://doi.org/10.4213/sm8184

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English version:
Sbornik: Mathematics, 2013, 204:9, 1239–1263

Bibliographic databases:

Document Type: Article
UDC: 517.956.45
MSC: 35K60
Received: 16.10.2012 and 02.04.2013

Citation: È. R. Andriyanova, F. Kh. Mukminov, “Stabilization of the solution of a doubly nonlinear parabolic equation”, Mat. Sb., 204:9 (2013), 3–28; Sb. Math., 204:9 (2013), 1239–1263

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb8184
• https://doi.org/10.4213/sm8184
• http://mi.mathnet.ru/eng/msb/v204/i9/p3

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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. L. M. Kozhevnikova, A. A. Leont'ev, “Solutions to higher-order anisotropic parabolic equations in unbounded domains”, Sb. Math., 205:1 (2014), 7–44
4. 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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