ASYMPTOTIC BEHAVIORS AND EXISTENCE OF TRAVELING WAVE SOLUTIONS TO THE KELLER-SEGEL MODEL WITH LOGARITHMIC SENSITIVITY

被引：2

作者：

LI, C. H. E. N. ^{[1
]}

Liu, J. I. A. N. G. ^{[1
]}

DU, Z. E. N. G. J., I ^{[1
]}

机构：

[1] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2023年 / 28卷 / 03期

关键词：

Keller-Segel model; traveling wave solutions; asymptotic behavior; geometric singular perturbation; invariant manifold; SINGULAR SENSITIVITY; CHEMOTAXIS SYSTEM; GLOBAL EXISTENCE; NONLINEAR STABILITY; HYPERBOLIC SYSTEM; BOUNDARY-LAYERS; BOUNDEDNESS; DIFFUSION; BACTERIA; BANDS;

D O I：

10.3934/dcdsb.2022146

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are concerned with the existence of traveling wave solutions for the Keller-Segel model with logarithmic sensitivity. By the Hopf-Cole transformation and traveling wave transformation, the degenerate Keller-Segel system is transformed into a singularly perturbed system. By constructing an invariant region to prove the existence of the traveling wave solutions for the degenerate system, we obtain the traveling wave solutions for Keller-Segel system with small parameter by using geometric singular perturbation theory and Fredholm theory. Finally, we discuss the asymptotic behaviors of the traveling wave solutions.

引用

页码：1771 / 1786

页数：16

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