Results 31 to 40 of about 496 (81)

Asymptotic behavior of global mild solutions to the Keller-Segel-Navier-Stokes system in Lorentz spaces

Advances in Nonlinear Analysis
The Keller-Segel-Navier-Stokes system in RN{{\mathbb{R}}}^{N} is considered, where N≥3N\ge 3. We show the existence and uniqueness of local mild solutions for arbitrary initial data and gravitational potential in scaling invariant Lorentz spaces ...
Takeuchi Taiki
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Singular sensitivity in a Keller-Segel-fluid system

, 2017
In bounded smooth domains $\Omega\subset\mathbb{R}^N$, $N\in\{2,3\}$, considering the chemotaxis--fluid system \[ \begin{cases} \begin{split} & n_t + u\cdot \nabla n &= \Delta n - \chi \nabla \cdot(\frac{n}{c}\nabla c) &\\ & c_t + u\cdot \nabla c ...
Black, Tobias, Lankeit, Johannes, Mizukami, Masaaki   +2 more
core   +1 more source

A degenerate migration-consumption model in domains of arbitrary dimension

Advanced Nonlinear Studies
In a smoothly bounded convex domain Ω⊂Rn ${\Omega}\subset {\mathbb{R}}^{n}$ with n ≥ 1, a no-flux initial-boundary value problem forut=Δuϕ(v),vt=Δv−uv, $$\begin{cases}_{t}={\Delta}\left(u\phi \left(v\right)\right),\quad \hfill \\ {v}_{t}={\Delta}v-uv ...
Winkler Michael
doaj   +1 more source

The fully parabolic multi-species chemotaxis system in $\mathbb{R}^{2}$

European Journal of Applied Mathematics
This article is devoted to the analysis of the parabolic–parabolic chemotaxis system with multi-components over $\mathbb{R}^2$ . The optimal small initial condition on the global existence of solutions for multi-species chemotaxis model in the ...
Ke Lin
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Analysis of a model describing bacterial colony expansion in radial geometry driven by chemotaxis

European Journal of Applied Mathematics
We investigate a recent model proposed in the literature elucidating patterns driven by chemotaxis, similar to viscous fingering phenomena. Notably, this model incorporates a singular advection term arising from a modified formulation of Darcy’s law.
Elio Espejo
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Stabilization in a chemotaxis system modelling T-cell dynamics with simultaneous production and consumption of signals

European Journal of Applied Mathematics
In a smoothly bounded domain $\Omega \subset \mathbb{R}^n$ , $n\ge 1$ , this manuscript considers the homogeneous Neumann boundary problem for the chemotaxis system \begin{eqnarray*} \left \{ \begin{array}{l} u_t = \Delta u - \nabla \cdot (
Youshan Tao, Michael Winkler
doaj   +1 more source

Global boundedness in a two-dimensional chemotaxis system with nonlinear diffusion and singular sensitivity

Advances in Nonlinear Analysis
In this study, we investigate the two-dimensional chemotaxis system with nonlinear diffusion and singular sensitivity: ut=∇⋅(uθ−1∇u)−χ∇⋅uv∇v,x∈Ω,t>0,vt=Δv−v+u+g(x,t),x∈Ω,t>0,(∗)\left\{\begin{array}{ll}{u}_{t}=\nabla \cdot \left({u}^{\theta -1}\nabla u ...
Ren Guoqiang, Zhou Xing
doaj   +1 more source

Travelling waves with continuous profile for hyperbolic Keller-Segel equation

European Journal of Applied Mathematics
This work describes a hyperbolic model for cell-cell repulsion with population dynamics. We consider the pressure produced by a population of cells to describe their motion.
Quentin Griette, Pierre Magal, Min Zhao
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Global dynamics for the generalised chemotaxis-Navier–Stokes system in $\mathbb{R}^3$

European Journal of Applied Mathematics
We consider the chemotaxis-Navier–Stokes system with generalised fluid dissipation in $\mathbb{R}^3$ : \begin{eqnarray*} \begin{cases} \partial _t n+u\cdot \nabla n=\Delta n- \nabla \cdot (\chi (c)n \nabla c),\\[5pt] \partial _t c+u \cdot \nabla
Qingyou He, Ling-Yun Shou, Leyun Wu
doaj   +1 more source

Keller–Segel type approximation for nonlocal Fokker–Planck equations in one-dimensional bounded domain

European Journal of Applied Mathematics
Numerous evolution equations with nonlocal convolution-type interactions have been proposed. In some cases, a convolution was imposed as the velocity in the advection term.
Hideki Murakawa, Yoshitaro Tanaka
doaj   +1 more source