相分离与损伤的温度依赖相场模型
摘要
本文研究热粘弹性材料中相分离与损伤的模型。本文的主要新颖之处在于，与文献中先前的工作（参见例如[C. Heinemann, C. Kraus: Existence results of weak solutions for Cahn-Hilliard systems coupled with elasticity and damage. Adv. Math. Sci. Appl. 21 (2011), 321--359]和[C. Heinemann, C. Kraus: Existence results for diffuse interface models describing phase separation and damage. European J. Appl. Math. 24 (2013), 179--211]）相反，我们在模型中包含了热过程，其与损伤、浓度和位移演化非线性耦合。更具体地，我们证明了“熵弱解”的存在性，借助于首先在[E. Feireisl: Mathematical theory of compressible, viscous, and heat conducting fluids. Comput. Math. Appl. 53 (2007), 461--490]中引入的、用于傅里叶-纳维-斯托克斯系统的可解性概念，随后被[E. Feireisl, H. Petzeltová, E. Rocca: Existence of solutions to a phase transition model with microscopic movements. Math. Methods Appl. Sci. 32 (2009), 1345--1369], [E. Rocca, R. Rossi: "Entropic" solutions to a thermodynamically consistent PDE system for phase transitions and damage. SIAM J. Math. Anal., 47 (2015), 2519--2586]用于研究相变和损伤的偏微分方程组。我们的全局时间存在性结果是通过在精心设计的时间离散格式中取极限得到的。
引用
@article{arxiv.1510.03755,
title = {A temperature-dependent phase-field model for phase separation and damage},
author = {C. Heinemann and C. Kraus and E. Rocca and R. Rossi},
journal= {arXiv preprint arXiv:1510.03755},
year = {2015}
}