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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 414590, 24 pages
http://dx.doi.org/10.1155/2012/414590
Research Article

Some Properties of Solutions for the Sixth-Order Cahn-Hilliard-Type Equation

Department of Mathematics, Jilin University, Changchun 130012, China

Received 10 July 2012; Revised 18 August 2012; Accepted 6 September 2012

Academic Editor: Ruediger Landes

Copyright © 2012 Zhao Wang and Changchun Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the initial boundary value problem for a sixth-order Cahn-Hilliard-type equation which describes the separation properties of oil-water mixtures, when a substance enforcing the mixing of the phases is added. We show that the solutions might not be classical globally. In other words, in some cases, the classical solutions exist globally, while in some other cases, such solutions blow up at a finite time. We also discuss the existence of global attractor.