Robinson, Michael Classification of heteroclinic orbits of semilinear parabolic equations with a polynomial nonlinearity. (English) Zbl 1217.35030 Electron. J. Differ. Equ. 2011, Paper No. 61, 10 p. (2011). 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 Keywords:heteroclinic connection; semilinear parabolic equation; equilibrium; gradient flow; finite energy constraint PDFBibTeX XMLCite \textit{M. Robinson}, Electron. J. Differ. Equ. 2011, Paper No. 61, 10 p. (2011; Zbl 1217.35030) Full Text: arXiv EuDML EMIS