Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 61, pp. 1-10.

Title: Classification of heteroclinic orbits of semilinear
       parabolic equations with a polynomial nonlinearity
       
Author: Michael Robinson (Univ. of Pennsylvania, Philadelphia, PA, USA)

Abstract:
 For a given semilinear parabolic equation with polynomial
 nonlinearity, many solutions blow up in finite time.  For a certain
 class of these equations, we show that some of the solutions which do
 not blow up actually tend to equilibria.  The characterizing property
 of such solutions is a finite energy constraint, which comes about
 from the fact that this class of equations can be written as the flow
 of the L^2 gradient of a certain functional.


Submitted August 26, 2010. Published May 10, 2011.
Math Subject Classifications: 35B40, 35K55.
Key Words: Heteroclinic connection; semilinear parabolic equation;
           equilibrium.