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A Note on the Cahn-Hilliard Equation in H1 (R N ) Involving Critical Exponent

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Cholewa, Jan W. and Rodríguez Bernal, Aníbal (2014) A Note on the Cahn-Hilliard Equation in H1 (R N ) Involving Critical Exponent. Mathematica Bohemica, 139 (2). pp. 269-283. ISSN 0862-7959

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Official URL: http://dml.cz/bitstream/handle/10338.dmlcz/143854/MathBohem_139-2014-2_13.pdf


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Abstract

We consider the Cahn-Hilliard equation in H1(RN ) with two types of critically growing nonlinearities: nonlinearities satisfying a certain limit condition as |u| → ∞ and logistic type nonlinearities. In both situations we prove the H2(RN )-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)


Item Type:Article
Uncontrolled Keywords:Initial value problem for higher order parabolic equations; asymptotic behavior of solutions; critical exponent
Subjects:Sciences > Mathematics > Differential equations
ID Code:33265
Deposited On:24 Sep 2015 06:49
Last Modified:12 Dec 2018 15:06

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