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Tr. Mat. Inst. Steklova, 2012, Volume 278, Pages 114–128 (Mi tm3395)  

This article is cited in 4 scientific papers (total in 4 papers)

Stabilization of solutions of an anisotropic quasilinear parabolic equation in unbounded domains

L. M. Kozhevnikovaa, F. Kh. Mukminovb

a Sterlitamak Branch of Bashkir State University, Sterlitamak, Russia
b M. Akmullah Bashkir State Pedagogical University, Ufa, Russia

Abstract: The first initial-boundary value problem with the homogeneous Dirichlet boundary condition and a compactly supported initial function is considered for a model second-order anisotropic parabolic equation in a cylindrical domain $D=(0,\infty)\times\Omega$. We find an upper bound that characterizes the dependence of the decay rate of solutions as $t\to\infty$ on the geometry of the unbounded domain $\Omega\subset\mathbb R_n$, $n\geq3$, and on nonlinearity exponents. We also obtain an estimate for the admissible decay rate of nonnegative solutions in unbounded domains; this estimate shows that the upper bound is sharp.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2012, 278, 106–120

Bibliographic databases:

Document Type: Article
UDC: 517.956.4
Received in February 2011

Citation: L. M. Kozhevnikova, F. Kh. Mukminov, “Stabilization of solutions of an anisotropic quasilinear parabolic equation in unbounded domains”, Differential equations and dynamical systems, Collected papers, Tr. Mat. Inst. Steklova, 278, MAIK Nauka/Interperiodica, Moscow, 2012, 114–128; Proc. Steklov Inst. Math., 278 (2012), 106–120

Citation in format AMSBIB
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\by L.~M.~Kozhevnikova, F.~Kh.~Mukminov
\paper Stabilization of solutions of an anisotropic quasilinear parabolic equation in unbounded domains
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2012
\vol 278
\pages 114--128
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3395}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3058788}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2012
\vol 278
\pages 106--120
\crossref{https://doi.org/10.1134/S0081543812060119}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84867342485}


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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. È. R. Andriyanova, F. Kh. Mukminov, “Stabilization of the solution of a doubly nonlinear parabolic equation”, Sb. Math., 204:9 (2013), 1239–1263  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. L. M. Kozhevnikova, A. A. Leont'ev, “Solutions to higher-order anisotropic parabolic equations in unbounded domains”, Sb. Math., 205:1 (2014), 7–44  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. 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
    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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