Results 11 to 20 of about 89 (89)

Asymptotic behavior of type I blowup solutions to a parabolic-elliptic system of drift-diffusion type [PDF]

, 2010
A Cauchy problem for a parabolic-elliptic system of drift-di usion type is considered. The problem is formally of the form Ut = r (rU Ur( ) 1U): This system describes a mass-conserving aggregation phenomenon including gravitational collapse and ...
Yoshikazu, Giga, Takasi, Senba, Noriko, Mizoguchi   +2 more
core   +2 more sources

Stability Analysis of a Model of Atherogenesis: An Energy Estimate Approach

Computational and Mathematical Methods in Medicine, Volume 9, Issue 2, Page 121-142, 2008., 2008
Atherosclerosis is a disease of the vasculature that is characterized by chronic inflammation and the accumulation of lipids and apoptotic cells in the walls of large arteries. This disease results in plaque growth in an infected artery typically leading to occlusion of the artery. Atherosclerosis is the leading cause of human mortality in the US, much
A. I. Ibragimov, C. J. McNeal, L. R. Ritter, J. R. Walton   +3 more
wiley   +1 more source

Attractiveness of Constant States in Logistic-Type Keller–Segel Systems Involving Subquadratic Growth Restrictions

Advanced Nonlinear Studies, 2020
The chemotaxis-growth ...
Winkler Michael
doaj   +1 more source

Global solvability in a three-dimensional Keller-Segel-Stokes system involving arbitrary superlinear logistic degradation

Advances in Nonlinear Analysis, 2020
The Keller-Segel-Stokes ...
Wang Yulan, Winkler Michael, Xiang Zhaoyin   +2 more
doaj   +1 more source

The role of superlinear damping in the construction of solutions to drift-diffusion problems with initial data in L1

Advances in Nonlinear Analysis, 2019
In bounded n-dimensional domains Ω, the Neumann problem for the parabolic ...
Winkler Michael
doaj   +1 more source

Boundedness and stabilization in a three-species chemotaxis-competition system with singular sensitivity

Advances in Nonlinear Analysis
This paper deals with the following fully parabolic chemotaxis system with singular sensitivity and Lotka–Volterra competition kineticsut=Δu−χ1∇⋅uz∇z+μ1u(1−u−a12v−a13ω),x∈Ω,t>0,vt=Δv−χ2∇⋅vz∇z+μ2v(1−a21u−v−a23ω),x∈Ω,t>0,ωt=Δω−χ3∇⋅ωz∇z+μ3ω(1−a31u−a32v−ω),x∈
Zhu Zhangsheng
doaj   +1 more source

Three-dimensional modeling of tumor angiogenesis: endothelial cell progression and therapeutic implications

Open Mathematics
We propose a three-dimensional mathematical model describing the dynamics of endothelial cells during tumor-induced angiogenesis. This framework extends our earlier one- and two-dimensional formulations by incorporating the three-dimensional spatial ...
Keleş Duman Melike, Pamuk Serdal
doaj   +1 more source

Chemotaxis-consumption system with Robin boundary conditions coupled to the (Navier–)Stokes equations

Advances in Nonlinear Analysis
In this paper, we consider the chemotaxis-consumption system on a bounded smooth domain Ω⊂Rn,n=2,3 ${\Omega}\subset {\mathbb{R}}^{n},n=2,3$ , with fluid ...
Kim Dongkwang, Ahn Jaewook
doaj   +1 more source

Boundedness and finite-time blow-up for the chemotaxis system with indirect signal production and flux limitation

Advances in Nonlinear Analysis
In this work, we consider a flux-limited chemotaxis model with indirect signal production and nonlinear diffusion,ut=∇⋅(D(u)∇u)−∇⋅(uf(|∇v|2)∇v)−k1u+k2w,x∈Ω,t>0,0=Δv−μ(t)+w,x∈Ω,t>0,wt=Δw−λ1w+λ2u,x∈Ω,t>0 $$\begin{cases}_{t}=\nabla \cdot \left(D\left(u ...
Tu Xinyu, Mu Chunlai, Minghua Zhang
doaj   +1 more source

A note on the global existence and boundedness of an N-dimensional parabolic-elliptic predator-prey system with indirect pursuit-evasion interaction

Open Mathematics
We investigate the two-species chemotaxis predator-prey system given by the following system: ut=Δu−χ∇⋅(u∇w)+u(λ1−μ1ur1−1+av),x∈Ω,t>0,vt=Δv+ξ∇⋅(v∇z)+v(λ2−μ2vr2−1−bu),x∈Ω,t>0,0=Δw−w+v,x∈Ω,t>0,0=Δz−z+u,x∈Ω,t>0,\left\{\begin{array}{ll}{u}_{t}=\Delta u-\chi \
Liu Ling
doaj   +1 more source