ANALYSIS FOR 3D DEGENERATE CAHN-LARCHÉ MODEL WITH PERIODIC BOUNDARY CONDITIONS

Lixian Zhao; Xingzhi Bian; Fang Cheng

doi:10.11948/20200250

2021 Volume 11 Issue 3

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Lixian Zhao, Xingzhi Bian, Fang Cheng. ANALYSIS FOR 3D DEGENERATE CAHN-LARCHÉ MODEL WITH PERIODIC BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1494-1519. doi: 10.11948/20200250

Citation:

Lixian Zhao, Xingzhi Bian, Fang Cheng. ANALYSIS FOR 3D DEGENERATE CAHN-LARCHÉ MODEL WITH PERIODIC BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1494-1519. doi: 10.11948/20200250

ANALYSIS FOR 3D DEGENERATE CAHN-LARCHÉ MODEL WITH PERIODIC BOUNDARY CONDITIONS

1.
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
2.
Zhejiang Nenggo Precision Manufacture Co., Ltd, Yongkang, Zhejiang, China
3.
Materials Genome Institute, Shanghai University, Shanghai 200444, China
4.
Department of Mathematics, Shanghai University, Shanghai 200444, China

Corresponding author: Email address: lee0014@shu.edu.cn(L. X. Zhao)

Abstract

Abstract

Our aim in this article is to study the existence of weak solutions to the degenerate Cahn-Larché model. Under appropriate assumptions on the degenerate mobility and chemical free energy density, we prove the existence of weak solutions to the approximate problem with positive mobility by applying the method of continuation of local solutions, then we use the solutions of approximate problem to approach the solutions of degenerate problem. Furthermore, we perform the numerical simulations to investigate the microstructure evolution during the spinodal decomposition by utilizing this model.
- Degenerate Cahn-Larché model /
- weak solutions /
- phase-field simulations
MSC: 35K65, 74N20

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References

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