论文标题
Cahn-Hilliard型系统与非线性扩散的抛物线层次趋化系统的收敛
Convergence of a Cahn-Hilliard type system to a parabolic-elliptic chemotaxis system with nonlinear diffusion
论文作者
论文摘要
本文介绍了具有非线性扩散的抛物线纤维化趋化系统。证明，存在Cahn-Hilliard系统的解决方案，是通过应用Colli-Visintin的抽象理论[Comm。偏微分方程15（1990），737-756]用于双重非线性进化包含，其中一些有界单调操作员和适当的下半连续凸函数的亚分类操作员（参见Colli-fukao [coli-fukao [J.Math。Anal。Anal。Anal。Appl。429（2015），1190-1190-1213]）。此外，Colli-Fukao [J.微分方程260（2016），6930-6959]通过传递到Cahn-Hilliard方程中的极限来确定非线性扩散方程的解决方案。但是，似乎尚未研究具有非线性扩散的趋化系统的Cahn-Hilliard方法。本文将试图通过将溶液传递到Cahn-Hilliard型趋化系统中的极限，从而将溶液的存在具有非线性扩散。
This paper deals with a parabolic-elliptic chemotaxis system with nonlinear diffusion. It was proved that there exists a solution of a Cahn-Hilliard system as an approximation of a nonlinear diffusion equation by applying an abstract theory by Colli-Visintin [Comm. Partial Differential Equations 15 (1990), 737-756] for a doubly nonlinear evolution inclusion with some bounded monotone operator and subdifferential operator of a proper lower semicontinuous convex function (cf. Colli-Fukao [J. Math. Anal. Appl. 429 (2015), 1190-1213]). Moreover, Colli-Fukao [J. Differential Equations 260 (2016), 6930-6959] established existence of solutions to the nonlinear diffusion equation by passing to the limit in the Cahn-Hilliard equation. However, Cahn-Hilliard approaches to chemotaxis systems with nonlinear diffusions seem not to be studied yet. This paper will try to derive existence of solutions to a parabolic-elliptic chemotaxis system with nonlinear diffusion by passing to the limit in a Cahn-Hilliard type chemotaxis system.
