Asymptotic limits of viscous Cahn–Hilliard equation with homogeneous Dirichlet boundary condition

In this paper, we are concerned with the asymptotic behavior of solutions for the viscous Cahn–Hilliard equations when parameters involved in the equations tend to zero. Namely, it is shown that solutions of the viscous Cahn–Hilliard equations converge to solutions of the Allen–Cahn equation, the Ca...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2022-08, Vol.512 (1), p.126106, Article 126106
Main Authors: Kagawa, Keiichiro, Ôtani, Mitsuharu
Format: Article
Language:English
Subjects:
Allen–Cahn equation
Asymptotic limits
Cahn–Hilliard equation
Dirichlet boundary condition
Viscous Cahn–Hilliard equation
Viscous diffusion equation
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Summary:In this paper, we are concerned with the asymptotic behavior of solutions for the viscous Cahn–Hilliard equations when parameters involved in the equations tend to zero. Namely, it is shown that solutions of the viscous Cahn–Hilliard equations converge to solutions of the Allen–Cahn equation, the Cahn–Hilliard equation, and the viscous diffusion equation, when suitable parameters tend to zero. Compared with the existing results, a much wider range of chemical potentials can be treated within our setting.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2022.126106