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Mat. Sb., 1998, Volume 189, Number 3, Pages 45–68 (Mi msb304)  

This article is cited in 11 scientific papers (total in 15 papers)

Asymptotic behaviour of the solutions of non-linear elliptic and parabolic systems in tube domains

Yu. V. Egorov, V. A. Kondrat'ev, O. A. Oleinik

M. V. Lomonosov Moscow State University

Abstract: The paper is devoted to the study of the asymptotic behaviour of solutions of weakly non-linear elliptic and parabolic systems of second-order equations. In particular, the behaviour as $t\to+\infty$ of the solution of a second-order non-linear parabolic equation satisfying a Neumann boundary condition at the boundary of a bounded Lipschitz domain is studied. The proofs are based on a result on the asymptotic equivalence of two systems of ordinary differential equations.


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English version:
Sbornik: Mathematics, 1998, 189:3, 359–382

Bibliographic databases:

UDC: 517.9
MSC: 35J65, 35K60
Received: 16.06.1997

Citation: Yu. V. Egorov, V. A. Kondrat'ev, O. A. Oleinik, “Asymptotic behaviour of the solutions of non-linear elliptic and parabolic systems in tube domains”, Mat. Sb., 189:3 (1998), 45–68; Sb. Math., 189:3 (1998), 359–382

Citation in format AMSBIB
\by Yu.~V.~Egorov, V.~A.~Kondrat'ev, O.~A.~Oleinik
\paper Asymptotic behaviour of the~solutions of non-linear elliptic and parabolic systems in tube domains
\jour Mat. Sb.
\yr 1998
\vol 189
\issue 3
\pages 45--68
\jour Sb. Math.
\yr 1998
\vol 189
\issue 3
\pages 359--382

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    2. T. D. Venttsel', V. S. Vladimirov, V. V. Zhikov, A. M. Il'in, V. A. Il'in, V. A. Kondrat'ev, L. D. Kudryavtsev, E. F. Mishchenko, S. M. Nikol'skii, Yu. S. Osipov, E. V. Radkevich, N. Kh. Rozov, V. A. Sadovnichii, L. D. Faddeev, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, A. A. Shkalikov, “Ol'ga Arsen'evna Oleinik (obituary)”, Russian Math. Surveys, 58:1 (2003), 161–172  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Filimonova I.V., “Asymptotic behaviour of positive solutions of a semilinear parabolic equation”, Russ. J. Math. Phys., 10:2 (2003), 234–237  mathscinet  zmath  isi  elib
    4. T. S. Khachlaev, “The asymptotic behaviour of solutions of a semilinear elliptic equation with increasing coefficient in a cylindrical domain”, Russian Math. Surveys, 59:2 (2004), 383–384  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. Egorov, YV, “On the asymptotic behavior of solutions to a nonlinear parabolic boundary value problem”, Doklady Mathematics, 70:1 (2004), 603  mathscinet  zmath  isi  elib
    6. M. V. Borsuk, “Second-order degenerate elliptic boundary value problems in nonsmooth domains”, Journal of Mathematical Sciences, 146:5 (2007), 6071–6212  mathnet  crossref  mathscinet  zmath  elib
    7. O. V. Besov, V. S. Vladimirov, V. V. Kozlov, S. M. Nikol'skii, Yu. S. Osipov, S. I. Pokhozhaev, V. A. Sadovnichii, “Vladimir Aleksandrovich Kondrat'ev (on his 70th birthday)”, Russian Math. Surveys, 61:6 (2006), 1189–1197  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. V. A. Kondrat'ev, “Asymptotic properties of solutions of semilinear second-order elliptic equations in cylindrical domains”, J. Math. Sci. (N. Y.), 135:1 (2006), 2666–2674  mathnet  crossref  mathscinet  zmath
    9. I. V. Filimonova, “On the behavior of solutions of a semilinear parabolic or elliptic equation satisfying a nonlinear boundary condition in a cylindrical domain”, J. Math. Sci. (N. Y.), 143:4 (2007), 3415–3428  mathnet  crossref  mathscinet
    10. V. A. Kondrat'ev, “On the Asymptotic Behavior of Solutions of Nonlinear Second-Order Parabolic Equations”, Proc. Steklov Inst. Math., 260 (2008), 172–184  mathnet  crossref  mathscinet  isi  elib  elib
    11. Yu. V. Egorov, V. A. Kondratiev, “Asymptotic behaviour of solutions of semilinear parabolic equations”, Sb. Math., 199:4 (2008), 539–556  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    12. Antontsev S., Díaz J.I., “On gradient estimates and other qualitative properties of solutions of nonlinear non autonomous parabolic systems”, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 103:1 (2009), 201–214  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    13. M. S. Agranovich, I. V. Astashova, L. A. Bagirov, V. V. Vlasov, V. V. Zhikov, Yu. S. Ilyashenko, V. V. Kozlov, A. A. Kon'kov, S. I. Pokhozhaev, E. V. Radkevich, N. Kh. Rozov, I. N. Sergeev, A. L. Skubachevskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Vladimir Alexandrovich Kondratiev. July 2, 1935 – March 11, 2010”, Journal of Mathematical Sciences, 190:1 (2013), 1–7  mathnet  crossref  mathscinet
    14. Surnachev M., “Asymptotic behaviour of solutions of nondivergence type semilinear elliptic equations in conical domains I”, Asymptot Anal, 71:4 (2011), 227–243  crossref  mathscinet  zmath  isi  elib
    15. S. A. Zabolotskii, “Asimptoticheskoe povedenie reshenii nelineinykh differentsialnykh uravnenii s eksponentsialno ekvivalentnymi pravymi chastyami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:2 (2016), 215–220  mathnet  crossref  mathscinet  elib
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