Well-posedness of solutions to a phase-field model for the martensitic phase transformations

Abstract

We study a phase-field model, which describes the transformations for the austenite-martensite and the multiple twinning in Martensite. The model consists of two nonlinear parabolic equations of second order. We first show the existence of local solutions to an initial-boundary value problem by utilizing the Banach fixed-point theorem. Then we verify the solutions is global. Finally we investigate the regularity and uniqueness of the solution.

Keywords:

• Phase-field model
• coupled parabolic equations
• well-posedness
• Banach fixed-point theorem

2020 Mathematics Subject Classifications:

• 82C26
• 35K55
• 35B65

Acknowledgments

We are thankful to Professor Peicheng Zhu for his inspiring discussions and helpful comments. The author would like to deeply thank all the reviewers for their insightful and constructive comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

Data sharing is not applicable to this article as no data sets were created or analyzed during the current study.

Additional information

Funding

This work was partly supported by Science and Technology Commission of Shanghai Municipality [grant number 20JC1413600].