Green’s Function of the Linearized Logarithmic Keller–Segel–Fisher/KPP System

Mathematical and Computational Applications

Zeng, Yanni¹  Rugamba, Jean² 

[1] Author to whom correspondence should be addressed.;Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA

关键词: Green’s function;    fundamental solution;    Cauchy problem;    Keller–Segel;    chemotaxis;    logarithmic sensitivity;    logistic growth;   

DOI  :  10.3390/mca23040056

学科分类：计算数学

来源: mdpi

【 摘 要 】

We consider a Keller–Segel type chemotaxis model with logarithmic sensitivity and logistic growth. The logarithmic singularity in the system is removed via the inverse Hopf–Cole transformation. We then linearize the system around a constant equilibrium state, and obtain a detailed, pointwise description of the Green’s function. The result provides a complete solution picture for the linear problem. It also helps to shed light on small solutions of the nonlinear system.

【 授权许可】

CC BY