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
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.
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Mathematics of the USSR-Sbornik, 1987, 56:2, 295–309
MSC: Primary 35A08, 35B32, 35K22, 35K55; Secondary 35B35, 35B40, 35K05, 35K57
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
\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.)
\jour Math. USSR-Sb.
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A. M. Ter-Krikorov, “On transition processes for the Van der Pol equation”, Comput. Math. Math. Phys., 47:6 (2007), 924–935
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