Classification of connecting solutions of semilinear parabolic equations

2007/09/17 by Michael Robinson, Robinson, Michael
Mathematics · #35B40 #35K55 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B40 #msc:35K55

paper · pdf · doi:10.48550/arxiv.0709.2705

arxiv created 2007/09/17 · arxiv updated 2009/12/01

Abstract

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 L² gradient of a certain functional.

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