We establish new convergence results, in strong topologies, for solutions of the parabolic-parabolic Keller–Segel system in the plane, to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under...

We obtain a priori estimates for the classical chemotaxis model of Patlak, Keller and Segel when a nonlinear diffusion or a nonlinear chemosensitivity is considered accounting for the finite size of the cells. We will show how entropy estimates give natural conditions on the nonlinearities implying the absence of blow-up for the solutions.

Fibrosis Michael J. Segel, Pazit Y. Cohen, Gabriel Izbicki, Reuven Or 2, Thomas G. Christensen3, Shulamit B. Wallach-Dayan, Raphael Breuer (1) Lung Cellular & Molecular Biology Laboratory−Institute of Pulmonology and (2) Bone Marrow Transplantation Department Hadassah University Hospital and Hebrew University-Hadassah Medical School Jerusalem, Israel and (3) Mallory Institute of Pathology, Depa...

Abstract In this paper, we focus on the one-dimensional Keller-Segel chemotaxis system in a random heterogeneous domain. We assume that the corresponding diffusion and chemotaxis coefficients are given by stationary ergodic processes, and apply methods pertaining to stochastic two-scale convergence to derive the homogenized macroscopic equations. Special attention is paid to developing efficien...

This paper deals with classical solutions to the parabolic-parabolic system \begin{align*} \begin{cases} u_t=\Delta (\gamma (v) u ) &\mathrm{in}\ \Omega\times(0,\infty), \\[1mm] v_t=\Delta v - + \displaystyle \frac{\partial u}{\partial \nu} = v}{\partial 0 &\mathrm{on}\ \partial\Omega \times (0,\infty), u(\cdot,0)=u_0, \ v(\cdot,0)=v_0 \Omega, \end{cases} \end{align*} where $\Omega$ is a smooth...

We establish new convergence results, in strong topologies, for solutions of the parabolic-parabolic Keller–Segel system in the plane, to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under...

In this paper, we study the asymptotic stability and hair-trigger effect for Cauchy problem of following parabolic-parabolic Keller-Segel system with logistic term$ \begin{equation} \left\{ \begin{aligned} &u_{t} = \Delta u-\chi \nabla\cdot\left ( u\nabla v \right )+u\left(a-b u\right)&x\in \mathbb{R}^{N},\, t>0,\\ &\tau v_{t} v+\lambda u-\mu v&x\in t>0, \end{aligned} \rig...

Abstract In the early 1970s, Keller and Segel proposed cross-diffusion system to describe phenomenon of spatial structures in biological through chemical induced processes ([93, 94]).

Spatially-distributed populations of various types of bacteria often display intricate spatial patterns that are thought to result from the cellular response to gradients of nutrients or other attractants. In the past decade a great deal has been learned about signal transduction, metabolism and movement in E. coli and other bacteria, but translating the individual-level behavior into populatio...