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

Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA
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Math. Comput. Appl. 2018, 23(4), 56; https://doi.org/10.3390/mca23040056
Received: 14 September 2018 / Revised: 1 October 2018 / Accepted: 1 October 2018 / Published: 3 October 2018
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PDF [317 KB, uploaded 17 October 2018]

Abstract

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. View Full-Text
Keywords: Green’s function; fundamental solution; Cauchy problem; Keller–Segel; chemotaxis; logarithmic sensitivity; logistic growth Green’s function; fundamental solution; Cauchy problem; Keller–Segel; chemotaxis; logarithmic sensitivity; logistic growth
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Rugamba, J.; Zeng, Y. Green’s Function of the Linearized Logarithmic Keller–Segel–Fisher/KPP System. Math. Comput. Appl. 2018, 23, 56.

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