Electron. J. Differential Equations, Vol. 2018 (2018), No. 76, pp. 1-13.

Existence of solutions for a quasi-linear phase separation of multi-component system

Dongpei Zhang, Ruikuan Liu

Abstract:
This article formulates a new model of the phase separation of multi-component system, which is a fourth-order quasi-linear evolution partial differential equation. By using the acute angle principle, we obtain a weak solution of the corresponding steady-state equations. In addition, we show that the quasi-linear dynamic equations have at least one global weak solution, based on the T-weakly continuous operators theory.

Submitted May 5, 2017. Published March 18, 2018.
Math Subject Classifications: 35J58, 35J62, 35K52, 35K59.
Key Words: Multi-component system; the acute angle principle; T-weakly continuous operators; global weak solution.

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Dongpei Zhang
Department of Mathematics
Sichuan University
Chengdu, Sichuan 610064, China
email: zhangdpscu@163.com
Ruikuan Liu
Department of Mathematics
Sichuan University
Chengdu, Sichuan 610064, China
email: liuruikuan2008@163.com

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