Geodesic
Classification of heteroclinic orbits of semilinear parabolic equations with a polynomial nonlinearity
Electronic Journal of Differential Equations, Tome 2011 (2011).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 35B40, 35K55
Keywords: heteroclinic connection, semilinear parabolic equation, equilibrium 
@article{EJDE_2011__2011__a76,
     author = {Robinson, Michael},
     title = {Classification of heteroclinic orbits of semilinear parabolic equations with a polynomial nonlinearity},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2011},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a76/}
}
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Robinson, Michael. Classification of heteroclinic orbits of semilinear parabolic equations with a polynomial nonlinearity. Electronic Journal of Differential Equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a76/