Analytical solutions for the viscous Cahn-Hilliard equation are considered. Existence and uniqueness of the solution are shown. The exponential decay of the solution inH 2-norm, which is an improvement of the result in Elliott and Zheng. We also compare the early stages of evolution of the viscous Cahn-Hilliard equation with that of the Cahn-Hilliard equation, which has been given as an open question in Novick-Cohen.
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The first author was supported by Korea Research Foundation under grant KRF-2001-002-D00036.
S. M. Choo received his BS and MS from Seoul National University. He earned his Ph.D. at Seoul National University under the direction of S.K. Chung. He has been at Ulsan University since September, 2001. His research interests is numerical analysis.
S. K. Chung received his BS from Seoul National University and MS from Sogang University. He earned his Ph.D. at The University of Texas ar Arlington under the supervision of R. Kannan. He has been at Seoul National University since 1987. His research interests is numerical analysis.
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Choo, S.M., Chung, S.K. Asymtotic behaviour of the viscous Cahn-Hilliard equation. JAMC 11, 143–154 (2003). https://doi.org/10.1007/BF02935727
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Key words and Phrases
- Viscous Cahn-Hilliard equation
- decay property
- comparison theorem