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
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