一类非局部Cahn-Hilliard-Keller-Segel方程解的存在性
Existence of Solutions for a Class of Nonlocal Cahn-Hilliard-Keller-Segel Equations
毛竣楠 1周彬 2王亚兴1
作者信息
- 1. 西南石油大学理学院,成都 610500
- 2. 西南石油大学理学院,成都 610500;西南石油大学人工智能研究院,成都 610500
- 折叠
摘要
本文将带有logistic源的Keller–Segel型反应扩散方程与具有源项和奇异势的非局部Cahn–Hilliard方程耦合, 提出一种新的相场-趋化耦合模型. 通过设计一个兼具势能正则化与浓度截断的双重逼近方案, 克服了奇异势能和交叉扩散项带来的数学困难, 利用一致能量估计与紧性方法为该耦合系统建立了全局弱解的存在性.
Abstract
This paper couples the Keller–Segel-type reaction–diffusion equations with a log-\\istic source to the nonlocal Cahn–Hilliard equation with source term and singular potential, thereby proposing a novel phase-field–chemotaxis coupled model. By devising a dual approx-\\imation scheme that incorporates both potential regularization and concentration truncation, we overcome the mathematical difficulties arising from the singular potential and the cross-di\\ffusion terms. Uniform energy estimates and compactness methods are employed to establish the existence of global weak solutions for the coupled system.关键词
应用数学/非局部Cahn–Hilliard方程/Keller–Segel模型/奇异势/正则化Key words
nonlocal Cahn–Hilliard equation/Keller–Segel model/singular potential/regularization引用本文复制引用
毛竣楠,周彬,王亚兴.一类非局部Cahn-Hilliard-Keller-Segel方程解的存在性[EB/OL].(2026-02-03)[2026-02-05].http://www.paper.edu.cn/releasepaper/content/202602-19.学科分类
数学
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