Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 16, pp. 1-17.

Title: A cell complex structure for the space of heteroclines 
      for a semilinear parabolic equation
   
Author: Michael Robinson (Univ. of Pennsylvania, Philadelphia, PA, USA)

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.