Geodesic
A note on the Cahn-Hilliard equation in $H^1(\mathbb R^N)$ involving critical exponent
Mathematica Bohemica, Tome 139 (2014) no. 2, pp. 269-283.

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We consider the Cahn-Hilliard equation in $H^1(\mathbb R^N)$ with two types of critically growing nonlinearities: nonlinearities satisfying a certain limit condition as $|u|\to \infty $ and logistic type nonlinearities. In both situations we prove the $H^2(\mathbb R^N)$-bound on the solutions and show that the individual solutions are suitably attracted by the set of equilibria. This complements the results in the literature; see J. W. Cholewa, A. Rodriguez-Bernal (2012).
DOI : 10.21136/MB.2014.143854
Classification : 35B33, 35B40, 35K30, 35K59
Keywords: initial value problem for higher order parabolic equations; asymptotic behavior of solutions; critical exponent 
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Cholewa, Jan W.; Rodriguez-Bernal, Anibal. A note on the Cahn-Hilliard equation in $H^1(\mathbb R^N)$ involving critical exponent. Mathematica Bohemica, Tome 139 (2014) no. 2, pp. 269-283. doi : 10.21136/MB.2014.143854. http://geodesic.mathdoc.fr/articles/10.21136/MB.2014.143854/

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