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arXiv:0709.2705 [math.AP]AbstractReferencesReviewsResources

Classification of connecting solutions of semilinear parabolic equations

Michael Robinson

Published 2007-09-17Version 1

For a given semilinear parabolic equation with polynomial nonlinearity, many solutions blow up in finite time. For a certain large 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 $L^2$ gradient of a certain functional.

Categories: math.AP
Subjects: 35B40, 35K55
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