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 タイトル: The dynamics of a degenerate reaction diffusion equation 著者: Angenent, Sigurd B. 発行日: 1994年 出版者: Graduate School of Mathematical Sciences, The University of Tokyo 掲載誌情報: Journal of Mathematical Sciences, The University of Tokyo. Vol. 1 (1994), No. 3, Page 471-524 抄録: We consider the initial-boundary value problem for a degenerate reaction diffusion equation consisting of the porous medium operator plus a nonlinear reaction term. The structure of the set of equilibria depends on the length of the spatial domain. There are two critical lengths $\scriptstyle 0L_1$. Using a topological argument we show existence of connecting orbits joining the unstable equilibrium with the two stable equilibria for $\scriptstyle L\in(L_0, L_1]$, when there are three equilibria. By showing that the principle of linearized stability can sometimes be applied with succes to degenerate parabolic equations, these connections are found to be unique for \$\scriptstyle L_0 URI: http://hdl.handle.net/2261/1576 ISSN: 13405705 出現カテゴリ: Journal of Mathematical Sciences, the University of TokyoJournal of Mathematical Sciences, the University of Tokyo

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