Geodesic
Construction of fundamental solutions of an abstract nonlinear parabolic equation in a~neighborhood of a~bifurcation point
Sbornik. Mathematics, Tome 56 (1987) no. 2, pp. 295-309

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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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     author = {A. A. Belolipetskii and A. M. Ter-Krikorov},
     title = {Construction of fundamental solutions of an abstract nonlinear parabolic equation in a~neighborhood of a~bifurcation point},
     journal = {Sbornik. Mathematics},
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A. A. Belolipetskii; A. M. Ter-Krikorov. Construction of fundamental solutions of an abstract nonlinear parabolic equation in a~neighborhood of a~bifurcation point. Sbornik. Mathematics, Tome 56 (1987) no. 2, pp. 295-309. http://geodesic.mathdoc.fr/item/SM_1987_56_2_a1/