Asymptotic behavior of the coupled Allen-Cahn/Cahn-Hilliard system with proliferation term

被引：0

作者：

Makki, Ahmad ^{[3
,5
]}

Mheich, Rim ^{[1
,4
]}

Petcu, Madalina ^{[1
]}

Talhouk, Raafat ^{[2
,4
]}

机构：

[1] Univ Poitiers, Lab Math & Applicat, UMR CNRS 7348, SP2MI, Blvd Marie & Pierre Curie Teleport 2, F-86962 Futuroscope, France

[2] De Vinci Res Ctr, De Vinci Higher Educ, Paris, France

[3] Lebanese Amer Univ, Dept Comp Sci & Math, Beirut, Lebanon

[4] Univ Libanaise, Fac Sci, Lab Math EDST, Hadat, Lebanon

[5] Univ Modena & Reggio Emilia, Dipartimento Sci & Metodi Ingn, Via Univ 4, I-41121 Modena, Italy

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2025年 / 548卷 / 01期

关键词：

Allen-Cahn/Cahn-Hilliard; Well-posedness; Proliferation term; Asymptotic behavior; Global attractor; Fractal dimension; FE-CR ALLOYS; SPINODAL DECOMPOSITION; COMPUTER-MODELS; ATOMIC-LEVEL; ORDER-DISORDER; CAHN SYSTEM; EQUATION;

D O I：

10.1016/j.jmaa.2025.129382

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we investigate the coupled Allen-Cahn/Cahn-Hilliard equations with a proliferation term, which can model the growth of cancerous tumors and other biological entities. We focus on establishing the existence, uniqueness, and regularity of solutions, as well as analyzing their asymptotic behavior, with particular attention to the existence of finite-dimensional attractors. The system is considered under Dirichlet boundary conditions, and we introduce assumptions on the proliferation term to ensure dissipativity. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页数：23

共 27 条

[1] Adaptive, second-order in time, primitive-variable discontinuous Galerkin schemes for a Cahn-Hilliard equation with a mass source [J].