The existence of global attractor for a Cahn-Hilliard/Allen-Cahn‎ ‎equation

Document Type : Research Paper

Authors

1 Department of Mathematics‎, ‎Jilin University‎, ‎Changchun 130012‎, ‎P.R. China and School of Science, Changchun University, Changchun 130022, P.R. China.

2 Department of Mathematics‎, ‎Jilin University‎, ‎Changchun 130012‎, ‎P.R. China.

3 Department of Mathematics‎, ‎Changchun Normal University‎, ‎Chang-chun‎ 130032, ‎P.R. China and Academy of Mathematics and Systems Science‎, ‎Chinese Academy of Sciences‎, ‎Beijing‎, ‎100190‎, ‎P‎.‎R‎. ‎China.

Abstract

In this paper, we consider a Cahn-Hillard/Allen-Cahn equation. By using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in $H^k(0<=k<5)$ space of this equation, and it attracts any bounded subset of $H^k(\omega)$ in the $H^k$-norm.

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References

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History

  • Receive Date: 19 September 2014
  • Revise Date: 17 March 2015
  • Accept Date: 17 March 2015

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