Electron. J. Diff. Equ.,
Vol. 2011 (2011), No. 61, pp. 110.
Classification of heteroclinic orbits of semilinear
parabolic equations with a polynomial nonlinearity
Michael Robinson
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.
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Michael Robinson
Mathematics Department,
University of Pennsylvania
209 S. 33rd Street
Philadelphia, PA 19104, USA
email: robim@math.upenn.edu

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