Results 51 to 60 of about 895 (106)

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
doaj   +1 more source

Asymptotic behaviour of global solutions to a model of cell invasion [PDF]

arXiv, 2009
In this paper we analyze a mathematical model focusing on key events of the cells invasion process. Global well-possedness and asymptotic behaviour of nonnegative solutions to the corresponding coupled system of three nonlinear partial differential equations are studied.
arxiv  

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

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 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

Derivation and travelling wave analysis of phenotype-structured haptotaxis models of cancer invasion

European Journal of Applied Mathematics
We formulate haptotaxis models of cancer invasion wherein the infiltrating cancer cells can occupy a spectrum of states in phenotype space, ranging from ‘fully mesenchymal’ to ‘fully epithelial’. The more mesenchymal cells are those that display stronger
Tommaso Lorenzi, Fiona R. Macfarlane, Kevin J. Painter   +2 more
doaj   +1 more source

A particle system approach to cell-cell adhesion models [PDF]

arXiv, 2016
We investigate micro-to-macroscopic derivations in two models of living cells, in presence to cell-cell adhesive interactions. We rigorously address two PDE-based models, one featuring non-local terms and another purely local, as a a result of a law of large numbers for stochastic particle systems, with moderate interactions in the sense of K ...
arxiv  

Cahn–Hilliard equations with singular potential, reaction term and pure phase initial datum

European Journal of Applied Mathematics
We consider local and nonlocal Cahn–Hilliard equations with constant mobility and singular potentials including, e.g., the Flory–Huggins potential, subject to no-flux (or periodic) boundary conditions.
Maurizio Grasselli, Luca Scarpa, Andrea Signori   +2 more
doaj   +1 more source

Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusion [PDF]

arXiv, 2016
We show the existence of locally bounded global solutions to the chemotaxis system \[ u_t = \nabla\cdot(D(u)\nabla u) - \nabla\cdot(\frac{u}{v} \nabla v) \] \[ v_t = \Delta v - uv \] with homogeneous Neumann boundary conditions and suitably regular positive initial data in smooth bounded domains $\Omega \subset \mathbb{R}^N$, $N\geq2$, for $D(u)\geq ...
arxiv  

The one-dimensional Keller-Segel model with fractional diffusion of cells [PDF]

, 2009
We investigate the one-dimensional Keller-Segel model where the diffusion is replaced by a non-local operator, namely the fractional diffusion with exponent $0<\alpha\leq 2$. We prove some features related to the classical two-dimensional Keller-Segel system: blow-up may or may not occur depending on the initial data.
arxiv   +1 more source