Global existence of weak solution to a phase‐field model on martensitic phase transformations. (9th September 2022)

• Record Type: Journal Article
• Authors: Yang, Manman; Wu, Fan; Zhu, Zixian
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 4(2023)
• Page Start: 3545
• Page End: 3559
• Publication Date: 2022-09-09
• Subjects: degenerate -- fixed‐point method -- global existence -- parabolic equations -- phase‐field model -- weak solution; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8708
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We introduce a mesoscale model capable of describing transformations between martensitic variants as well as twinning. The model consists of two nonlinear parabolic equations of second order, and one of equations is degenerate. We prove the existence of global‐in‐time solutions to an initial‐boundary value problem in one space dimension of this model.