Global Attractor for a Class of Sixth-Order Viscous Cahn-Hilliard Equation in an Unbounded Domain
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In this paper, we consider the existence of global attractor for a class of sixth-order Cahn-Hilliard equation with a nonlinear diffusion and viscous effects in an infinite domain. Due to the noncompactness of operators, we use weighted Sobolev spaces to prove that the semigroup generated by the equation has the global attractor in a suitable space.
KeywordsSixth-order viscous Cahn-Hilliard equation Weighted Sobolev space Semigroup Global attractor
Mathematics Subject Classification (2010)Primary: 35B40, 35B41 Secondary: 35B65
This work was done when Dr. Zhao was visiting the Institute of Mathematics for Industry of Kyushu University in 2017. He appreciate the hospitality of Prof. Fukumoto, MS. Sasaguri, and IMI.
ND was supported by the Natural Science Foundation of Jiangsu Province of China (grant no. BK20170172) and China Postdoctoral Science Foundation (grant No. 2017M611684 ). XZ was supported by Natural Science Foundation of Jiangsu Province (grant no. BK20140130) and China Postdoctoral Science Foundation (grant no. 2015M58 1689).
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