一类相变模型的弱解存在性的研究
Existence of Weak Solutions for a Class of Phase Field Models
DOI: 10.12677/PM.2020.107080, PDF,   
作者: 陈 梅：上海大学，材料基因组工程研究院，上海
关键词: 弱解的存在性；序参数；巴拿赫不动点定理；Existence of Weak Solutions； Order Parameter； Banach’s Fixed Point Theorem
摘要: 本文在忽略弹性效应的情况下，研究了一类Neumann边界条件下的序参数不守恒的相场模型。通过引入一个参数κ构造一个修正模型，然后借助巴拿赫不动点定理、Aubin-Lions引理和一系列先验估计，最终得到该模型弱解的整体存在性。
Abstract: We shall investigate a phase-field model with a non-conserved order parameter which is under Neumann boundary conditions and omitting the effect of elasticity. By introducing a parameter κ to construct a modified model, and then using Banach’s fixed point Theorem, Aubin-Lions lemma and a series of a-priori estimates, the existence of global weak solutions to the model is finally obtained.
文章引用：陈梅. 一类相变模型的弱解存在性的研究[J]. 理论数学, 2020, 10(7): 666-679. https://doi.org/10.12677/PM.2020.107080

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