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.