Electron. J. Diff. Eqns.,
Vol. 2009(2009), No. 16, pp. 117.
A cell complex structure for the space of heteroclines
for a semilinear parabolic equation
Michael Robinson
Abstract:
It is well known that for many semilinear parabolic equations there is
a global attractor which has a cell complex structure with finite
dimensional cells. Additionally, many semilinear parabolic equations
have equilibria with finite dimensional unstable manifolds. In this
article, these results are unified to show that for a specific
parabolic equation on an unbounded domain, the space of heteroclinic
orbits has a cell complex structure with finite dimensional cells.
The result depends crucially on the choice of spatial dimension and
the degree of the nonlinearity in the parabolic equation, and thereby
requires some delicate treatment.
Submitted January 5, 2009. Published January 16, 2009.
Math Subject Classifications: 35B40, 35K55.
Key Words: Eternal solution; heteroclinic connection; cell complex;
semilinear parabolic equation; equilibrium.
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Michael Robinson
University of Pennsylvania Department of Mathematics
David Rittenhouse Laboratory
209 South 33rd treet
Philadelphia, PA 19104, USA
email: robim@math.upenn.edu

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