On the Conserved Caginalp Phase-Field System with Logarithmic Potentials Based on the Maxwell-Cattaneo Law with Two Temperatures

被引：3
|
作者：
Makki, Ahmad [2 ]
Miranville, Alain [1 ,2 ,3 ,4 ]
Sadaka, Georges [5 ]
机构：
[1] Henan Normal Univ, Sch Math & Informat Sci, Xinxiang, Henan, Peoples R China
[2] Univ Poitiers, Lab Math & Applicat, UMR CNRS 7348, SP2MI Blvd Marie & Pierre Curie Teleport 2, F-86962 Futuroscope, France
[3] Fudan Univ, Shanghai, Peoples R China
[4] Xiamen Univ, Sch Math Sci, Xiamen, Fujian, Peoples R China
[5] Univ Rouen Normandie, Lab Math Raphal Salem, CNRS, UMR 6085, Ave Univ,BP 12, F-76801 St Etienne Du Rouvray, France
来源：
APPLIED MATHEMATICS AND OPTIMIZATION | 2021年 / 84卷 / 02期
关键词：
Caginalp system; Maxwell-Cattaneo law; Two temperatures; Logarithmic nonlinear terms; Well-posedness; Dissipativity; Global attractor; Simulations; LONG-TIME BEHAVIOR; MODEL; CONVERGENCE; ATTRACTORS; EQUATION;
D O I：
10.1007/s00245-020-09677-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Our aim in this article is to study generalizations of the conserved Caginalp phase-field system based on the Maxwell-Cattaneo law with two temperatures for heat conduction and with logarithmic nonlinear terms. We obtain well-posedness results and study the asymptotic behavior of the associated system. In particular, we prove the existence of the global attractor and prove the strict separation to the pure phases in two space dimensions. Furthermore, we give some numerical simulations, obtained with the FreeFem++ software [23], comparing the conserved Caginalp phase-field type model with regular and with logarithmic nonlinear terms.
引用
收藏
页码：1285 / 1316
页数：32
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