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Mat. Sb. (N.S.), 1985, Volume 128(170), Number 3(11), Pages 306–320 (Mi msb2161)  

This article is cited in 1 scientific paper (total in 1 paper)

Construction of fundamental solutions of an abstract nonlinear parabolic equation in a neighborhood of a bifurcation point

A. A. Belolipetskii, A. M. Ter-Krikorov


Abstract: A nonlinear equation of parabolic type with functions taking values in a Banach space is studied. A family of solutions called a fundamental family is constructed in a neighborhood of a bifurcation point. It is shown that as $t\to\infty$ the fundamental solutions tend either to zero or to some steady-state solution of the nonlinear equation. Conditions are investigated under which the solutions of Cauchy problems behave like fundamental solutions.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Sbornik, 1987, 56:2, 295–309

Bibliographic databases:

UDC: 517.95
MSC: Primary 35A08, 35B32, 35K22, 35K55; Secondary 35B35, 35B40, 35K05, 35K57
Received: 27.04.1984

Citation: A. A. Belolipetskii, A. M. Ter-Krikorov, “Construction of fundamental solutions of an abstract nonlinear parabolic equation in a neighborhood of a bifurcation point”, Mat. Sb. (N.S.), 128(170):3(11) (1985), 306–320; Math. USSR-Sb., 56:2 (1987), 295–309

Citation in format AMSBIB
\Bibitem{BelTer85}
\by A.~A.~Belolipetskii, A.~M.~Ter-Krikorov
\paper Construction of fundamental solutions of an abstract nonlinear parabolic equation in a~neighborhood of a~bifurcation point
\jour Mat. Sb. (N.S.)
\yr 1985
\vol 128(170)
\issue 3(11)
\pages 306--320
\mathnet{http://mi.mathnet.ru/msb2161}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=815266}
\zmath{https://zbmath.org/?q=an:0658.35046|0607.34056}
\transl
\jour Math. USSR-Sb.
\yr 1987
\vol 56
\issue 2
\pages 295--309
\crossref{https://doi.org/10.1070/SM1987v056n02ABEH003037}


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    This publication is cited in the following articles:
    1. A. M. Ter-Krikorov, “On transition processes for the Van der Pol equation”, Comput. Math. Math. Phys., 47:6 (2007), 924–935  mathnet  crossref  elib  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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