The steady states and convergence to equilibria for a 1-D chemotaxis model with volume-filling effect

2009 ◽  
pp. n/a-n/a ◽  
Author(s):  
Yanyan Zhang
Keyword(s):  
Steady States ◽  
Chemotaxis Model ◽  
Volume Filling ◽  
Convergence To Equilibria

scholarly journals An eigenvalue problem arising from spiky steady states of a minimal chemotaxis model

2014 ◽  
Vol 420 (1) ◽  
pp. 684-704 ◽  
Author(s):  
Yajing Zhang ◽  
Xinfu Chen ◽  
Jianghao Hao ◽  
Xin Lai ◽  
Cong Qin
Keyword(s):  
Eigenvalue Problem ◽  
Steady States ◽  
Chemotaxis Model

Global and exponential attractor of the repulsive Keller–Segel model with logarithmic sensitivity

2020 ◽  
pp. 1-19
Author(s):  
LIN CHEN ◽  
FANZE KONG ◽  
QI WANG
Keyword(s):  
Initial Data ◽  
Steady States ◽  
Sensitivity Function ◽  
Exponential Attractor ◽  
Physical Stimulus ◽  
Chemotaxis Model ◽  
Constant Solution ◽  
Cellular Aggregation ◽  
Logarithmic Sensitivity ◽  
Well Posed

We consider a Keller–Segel model that describes the cellular chemotactic movement away from repulsive chemical subject to logarithmic sensitivity function over a confined region in ${{\mathbb{R}}^n},\,n \le 2$ . This sensitivity function describes the empirically tested Weber–Fecher’s law of living organism’s perception of a physical stimulus. We prove that, regardless of chemotaxis strength and initial data, this repulsive system is globally well-posed and the constant solution is the global and exponential in time attractor. Our results confirm the ‘folklore’ that chemorepulsion inhibits the formation of non-trivial steady states within the logarithmic chemotaxis model, hence preventing cellular aggregation therein.

Global Bifurcation of Stationary Solutions for a Volume-Filling Chemotaxis Model with Logistic Growth

2020 ◽  
Vol 30 (13) ◽  
pp. 2050182
Author(s):  
Yaying Dong ◽  
Shanbing Li
Keyword(s):  
Bifurcation Theory ◽  
Global Bifurcation ◽  
Neumann Boundary ◽  
Stationary Solutions ◽  
Logistic Growth ◽  
Fredholm Operators ◽  
Chemotaxis Model ◽  
Volume Filling ◽  
Constant Solution ◽  
Global Bifurcation Theory

In this paper, we show how the global bifurcation theory for nonlinear Fredholm operators (Theorem 4.3 of [Shi & Wang, 2009]) and for compact operators (Theorem 1.3 of [Rabinowitz, 1971]) can be used in the study of the nonconstant stationary solutions for a volume-filling chemotaxis model with logistic growth under Neumann boundary conditions. Our results show that infinitely many local branches of nonconstant solutions bifurcate from the positive constant solution [Formula: see text] at [Formula: see text]. Moreover, for each [Formula: see text], we prove that each [Formula: see text] can be extended into a global curve, and the projection of the bifurcation curve [Formula: see text] onto the [Formula: see text]-axis contains [Formula: see text].

scholarly journals Pattern formation for a volume-filling chemotaxis model with logistic growth

2017 ◽  
Vol 448 (2) ◽  
pp. 885-907 ◽  
Author(s):  
Yazhou Han ◽  
Zhongfang Li ◽  
Jicheng Tao ◽  
Manjun Ma
Keyword(s):  
Pattern Formation ◽  
Logistic Growth ◽  
Chemotaxis Model ◽  
Volume Filling

A 1-d quasilinear nonuniform parabolic chemotaxis model with volume-filling effect

2013 ◽  
Vol 83 (1-2) ◽  
pp. 101-125 ◽  
Author(s):  
Yanyan Zhang ◽  
Songmu Zheng
Keyword(s):  
Chemotaxis Model ◽  
Volume Filling

scholarly journals Nonlinear Instability for a Volume-Filling Chemotaxis Model with Logistic Growth

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Haiyan Gao ◽  
Shengmao Fu
Keyword(s):  
Nonlinear Evolution ◽  
Initial Perturbation ◽  
Neumann Boundary ◽  
Logistic Growth ◽  
Nonlinear Instability ◽  
Chemotaxis Model ◽  
Linear Dynamics ◽  
Volume Filling ◽  
Neumann Boundary Value Problem ◽  
Time Period

This paper deals with a Neumann boundary value problem for a volume-filling chemotaxis model with logistic growth in ad-dimensional boxTd=(0,π)d  (d=1,2,3). It is proved that given any general perturbation of magnitudeδ, its nonlinear evolution is dominated by the corresponding linear dynamics along a finite number of fixed fastest growing modes, over a time period of the orderln⁡(1/δ). Each initial perturbation certainly can behave drastically different from another, which gives rise to the richness of patterns.

scholarly journals On convergence to equilibria for the Keller–Segel chemotaxis model

2007 ◽  
Vol 236 (2) ◽  
pp. 551-569 ◽  
Author(s):  
Eduard Feireisl ◽  
Philippe Laurençot ◽  
Hana Petzeltová
Keyword(s):  
Chemotaxis Model ◽  
Convergence To Equilibria

Traveling wavefronts for a reaction-diffusion-chemotaxis model with volume-filling effect

2017 ◽  
Vol 32 (1) ◽  
pp. 108-116
Author(s):  
Man-jun Ma ◽  
Hui Li ◽  
Mei-yan Gao ◽  
Ji-cheng Tao ◽  
Ya-zhou Han
Keyword(s):  
Reaction Diffusion ◽  
Chemotaxis Model ◽  
Volume Filling
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