Korean J. Math.  Vol 22, No 4 (2014)  pp.621-632
DOI: https://doi.org/10.11568/kjm.2014.22.4.621

Dynamical bifurcation of the one-dimensional convective Cahn-Hilliard equation

Yuncherl Choi


In this paper, we study the dynamical behavior of the one-dimensional convective Cahn-Hilliard equation(CCHE) on a periodic cell $[-\pi,\pi]$.
We prove that as the control parameter passes through the critical number,the CCHE bifurcates from the trivial solution to an attractor.
We describe the bifurcated attractor in detail which gives the final patterns of solutions near the trivial solution.


convective Cahn-Hilliard equation, dynamic bifurcation, center manifold reduction

Subject classification

37G35, 35B32


This work was supported by the Research Grant of Kwangwoon University in 2014.

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