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

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 descrip...

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Bibliographic Details
Published in:Mathematical and computational applications Vol. 23; no. 4; p. 56
Main Authors: Rugamba, Jean, Zeng, Yanni
Format: Journal Article
Language:English
Published: MDPI AG 01-12-2018
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Summary: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.
ISSN:2297-8747
2297-8747
DOI:10.3390/mca23040056