On the steady state bifurcation of the Cahn-Hilliard/Allen-Cahn system

Shixing Li; Dongming Yan

doi:10.3934/dcdsb.2018301

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2019, Volume 24, Issue 7: 3077-3088. Doi: 10.3934/dcdsb.2018301

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On the steady state bifurcation of the Cahn-Hilliard/Allen-Cahn system

Shixing Li and
Dongming Yan^,

School of Data Sciences, Zhejiang University of Finance & Economics, Hangzhou, 310018, China

* Corresponding author E-mail: dmyan@zufe.edu.cn(Dongming Yan)
* Corresponding author E-mail: dmyan@zufe.edu.cn(Dongming Yan)

Received: February 28, 2018

Early access: October 2018

Published: May 2019

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Abstract

In this paper, the steady state bifurcation of the Cahn-Hilliard/Allen-Cahn system is investigated. By using the Lyapunov-Schmidt method, combining with the implicit function theorem, we prove that this system bifurcates from the trivial solution to the nontrivial solution branch as parameter crosses certain critical value. The expression of bifurcated solution is also obtained.

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Mathematics Subject Classification: Primary: 35G60; Secondary: 35Q56.

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References

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