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Mat. Sb., 2010, Volume 201, Number 9, Pages 3–26 (Mi msb7602)  

This article is cited in 11 scientific papers (total in 11 papers)

Stabilization of solutions of quasilinear second order parabolic equations in domains with non-compact boundaries

R. Kh. Karimova, L. M. Kozhevnikovab

a Institute of Applied Research
b Sterlitamak State Pedagogical Academy

Abstract: The first mixed problem with homogeneous Dirichlet boundary condition and initial function with compact support is considered for quasilinear second order parabolic equations in a cylindrical domain $D=(0,\infty)\times\Omega$. Upper bounds are obtained, which give the rate of decay of the solutions as $t\to\infty$ as a function of the geometry of the unbounded domain $\Omega\subset \mathbb R_n$, $n\ge 2$.
Bibliography: 18 titles.

Keywords: first mixed problem, quasilinear parabolic equations, unbounded domain, stabilization of the solution, geometric characteristic.

DOI: https://doi.org/10.4213/sm7602

Full text: PDF file (632 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2010, 201:9, 1249–1271

Bibliographic databases:

UDC: 517.956.4
MSC: 35S15, 35B40
Received: 16.07.2009 and 08.04.2010

Citation: R. Kh. Karimov, L. M. Kozhevnikova, “Stabilization of solutions of quasilinear second order parabolic equations in domains with non-compact boundaries”, Mat. Sb., 201:9 (2010), 3–26; Sb. Math., 201:9 (2010), 1249–1271

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, F. Kh. Mukminov, “Otsenka snizu skorosti ubyvaniya resheniya parabolicheskogo uravneniya s dvoinoi nelineinostyu”, Ufimsk. matem. zhurn., 3:3 (2011), 3–14  mathnet  mathscinet  zmath
    2. V. F. Gilimshina, F. Kh. Mukminov, “Ob ubyvanii resheniya vyrozhdayuschegosya lineinogo parabolicheskogo uravneniya”, Ufimsk. matem. zhurn., 3:4 (2011), 43–56  mathnet  zmath
    3. L. M. Kozhevnikova, A. A. Leontev, “Otsenki resheniya anizotropnogo parabolicheskogo uravneniya s dvoinoi nelineinostyu”, Ufimsk. matem. zhurn., 3:4 (2011), 64–85  mathnet  zmath
    4. L. M. Kozhevnikova, F. Kh. Mukminov, “Stabilization of solutions of an anisotropic quasilinear parabolic equation in unbounded domains”, Proc. Steklov Inst. Math., 278 (2012), 106–120  mathnet  crossref  mathscinet  isi  elib  elib
    5. 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  mathnet  crossref
    6. L. M. Kozhevnikova, A. A. Leontiev, “Decay of solution of anisotropic doubly nonlinear parabolic equation in unbounded domains”, Ufa Math. J., 5:1 (2013), 63–82  mathnet  crossref  mathscinet  elib
    7. 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
    8. 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
    9. 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
    10. D. Andreucci, A. F. Tedeev, “The Cauchy-Dirichlet problem for the porous media equation in cone-like domains”, SIAM J. Math. Anal., 46:2 (2014), 1427–1455  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    11. 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
  • Математический сборник Sbornik: Mathematics (from 1967)
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