Global Regularity versus Infinite-Time Singularity Formation in a Chemotaxis Model with Volume-Filling Effect and Degenerate Diffusion

2012 ◽  
Vol 44 (5) ◽  
pp. 3502-3525 ◽  
Author(s):  
Zhi-An Wang ◽  
Michael Winkler ◽  
Dariusz Wrzosek
Keyword(s):  
Global Regularity ◽  
Degenerate Diffusion ◽  
Singularity Formation ◽  
Infinite Time ◽  
Time Singularity ◽  
Chemotaxis Model ◽  
Volume Filling

scholarly journals Finite-time singularity versus global regularity for hyper-viscous Hamilton–Jacobi-like equations

Nonlinearity ◽  
2003 ◽  
Vol 16 (6) ◽  
pp. 1967-1989 ◽  
Author(s):  
Hamid Bellout ◽  
Said Benachour ◽  
Edriss S Titi
Keyword(s):  
Finite Time ◽  
Global Regularity ◽  
Time Singularity ◽  
Finite Time Singularity

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 The Singularity Formation on the Coupled Burgers–Constantin–Lax–Majda System with the Nonlocal Term

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Linrui Li ◽  
Shu Wang
Keyword(s):  
Initial Data ◽  
Finite Time ◽  
Smooth Solution ◽  
Blow Up ◽  
Nonlocal Term ◽  
Convection Term ◽  
Large Initial Data ◽  
Singularity Formation ◽  
Time Singularity ◽  
Finite Time Singularity

In this paper, we study the finite-time singularity formation on the coupled Burgers–Constantin–Lax–Majda system with the nonlocal term, which is one nonlinear nonlocal system of combining Burgers equations with Constantin–Lax–Majda equations. We discuss whether the finite-time blow-up singularity mechanism of the system depends upon the domination between the CLM type’s vortex-stretching term and the Burgers type’s convection term in some sense. We give two kinds of different finite-time blow-up results and prove the local smooth solution of the nonlocal system blows up in finite time for two classes of large initial data.

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