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
雑誌名
Journal of mathematical sciences, the University of Tokyo
巻
1
号
3
ページ
471 - 524
発行年
1994
ISSN
13405705
書誌レコードID
AA11021653
フォーマット
application/pdf
日本十進分類法
415
Mathematical Reviews Number
MR1322689
Mathmatical Subject Classification
35B32(MSC1991)
35B40(MSC1991)
58F10(MSC1991)
出版者
Graduate School of Mathematical Sciences, The University of Tokyo
The dynamics of a degenerate reaction diffusion equation
jms010301.pdf
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