Geodesic
Classification of heteroclinic orbits of semilinear parabolic equations with a polynomial nonlinearity
Electronic journal of differential equations, Tome 2011 (2011)
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},
     year = {2011},
     volume = {2011},
     zbl = {1217.35030},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a76/}
}
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%A Robinson,  Michael
%T Classification of heteroclinic orbits of semilinear parabolic equations with a polynomial nonlinearity
%J Electronic journal of differential equations
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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/