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Classification of heteroclinic orbits of semilinear parabolic equations with a polynomial nonlinearity. (English) Zbl 1217.35030

Summary: 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.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
37C29 Homoclinic and heteroclinic orbits for dynamical systems
35K58 Semilinear parabolic equations
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