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Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials

Eden, A, Kalantarov, VK and Zelik, SV (2012) Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials Journal of Mathematical Physics, 54.

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Abstract

We study initial boundary value problems for the convective Cahn-Hilliard equation $\Dt u +\px^4u +u\px u+\px^2(|u|^pu)=0$. It is well-known that without the convective term, the solutions of this equation may blow up in finite time for any $p>0$. In contrast to that, we show that the presence of the convective term $u\px u$ in the Cahn-Hilliard equation prevents blow up at least for $0<p<\frac49$. We also show that the blowing up solutions still exist if $p$ is large enough ($p\ge2$). The related equations like Kolmogorov-Sivashinsky-Spiegel equation, sixth order convective Cahn-Hilliard equation, are also considered.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Eden, AUNSPECIFIEDUNSPECIFIED
Kalantarov, VKUNSPECIFIEDUNSPECIFIED
Zelik, SVUNSPECIFIEDUNSPECIFIED
Date : 16 August 2012
Identification Number : 10.1063/1.4798786
Related URLs :
Additional Information : This is an arXiv version of the paper.
Depositing User : Symplectic Elements
Date Deposited : 07 Jan 2015 18:12
Last Modified : 08 Jan 2015 02:33
URI: http://epubs.surrey.ac.uk/id/eprint/806840

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