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We consider a stochastic Keller-Segel-Navier-Stokes system in $R^2$ describing the collective motion of cells in an ambient stochastic fluid flow, where the cells are attracted by a chemical substance and transported by the ambient fluid…

Analysis of PDEs · Mathematics 2026-05-19 Fanze Kong , Chen-Chih Lai , Krutika Tawri

We consider a generalized class of Keller-Segel models describing the chemotaxis of biological populations (bacteria, amoebae, endothelial cells, social insects,...). We show the analogy with nonlinear mean field Fokker-Planck equations and…

Biological Physics · Physics 2016-11-23 Pierre-Henri Chavanis

We study an one{dimensional quasilinear system proposed by J. Tello and M. Winkler [19] which models the population dynamics of two competing species attracted by the same chemical. The kinetics terms of the interacting species are chosen…

Analysis of PDEs · Mathematics 2016-11-25 Jia Hu , Qi Wang , Jingyue Yang , Lu Zhang

As a class of nonlinear partial differential equations, the Keller-Segel system is widely used to model chemotaxis in biology. In this paper, we present the construction and analysis of a decoupled linear, mass-conservative, block-centered…

Numerical Analysis · Mathematics 2025-01-24 Jie Xu , Hongfei Fu

This paper investigates the formation of time--periodic and stable patterns of a two--competing--species Keller--Segel chemotaxis model with a focus on the effect of cellular growth. We carry out rigorous Hopf bifurcation analysis to obtain…

Analysis of PDEs · Mathematics 2017-07-11 Qi Wang , Jingyue Yang , Lu Zhang

We study the regularity and large-time behavior of a crowd of species driven by chemo-tactic interactions. What distinguishes the different species is the way they interact with the rest of the crowd: the collective motion is driven by…

Analysis of PDEs · Mathematics 2021-08-25 Siming He , Eitan Tadmor

Chemotaxis is a fundamental guidance mechanism of cells and organisms, responsible for attracting microbes to food, embryonic cells into developing tissues, immune cells to infection sites, animals towards potential mates, and…

Quantitative Methods · Quantitative Biology 2018-06-26 K. J. Painter

The Keller--Segel PDE is a model for chemotaxis known to exhibit possible finite-time blow-up. Following a seminal work by Tello and Winkler, a logistic damping term is added in this PDE and local well-posedness of mild solutions is proven.…

Probability · Mathematics 2025-12-24 Thomas Cavallazzi , Alexandre Richard , Milica Tomasevic

We study radial solutions in a ball of $\mathbb{R}^N$ of a semilinear, parabolic-elliptic Patlak-Keller-Segel system with a nonlinear sensitivity involving a critical power. For $N = 2$, the latter reduces to the classical linear model,…

Analysis of PDEs · Mathematics 2015-06-11 Alexandre Montaru

In this paper we deal with diffusive relaxation limits of nonlinear systems of Euler type modeling chemotactic movement of cells toward Keller--Segel type systems. The approximating systems are either hyperbolic--parabolic or…

Analysis of PDEs · Mathematics 2008-07-25 M. Di Francesco , D. Donatelli

Chemotaxis allows single cells to self-organize at the population level, as classically described by Keller-Segel models. We show that chemotactic aggregation can be understood using a generalized Maxwell construction based on the balance…

Soft Condensed Matter · Physics 2025-11-18 Henrik Weyer , David Muramatsu , Erwin Frey

Consider a class of chemotaxis-fluid model incorporating a volume-filling effect in the sense of Painter and Hillen (Can. Appl. Math. Q. 2002; 10(4): 501-543), which is a supercritical parabolic-elliptic Keller-Segel system. As shown by…

Analysis of PDEs · Mathematics 2024-10-04 Lili Wang , Wendong Wang , Yi Zhang

Populations can become spatially organised through chemotaxis autoattraction, wherein population members release their own chemoattractant. Standard models of this process usually assume phenotypic homogeneity, but recent studies have shed…

Populations and Evolution · Quantitative Biology 2025-06-05 Tommaso Lorenzi , Kevin J. Painter

Simulations are performed to investigate the nonlinear dynamics of a (2+1)-dimensional chemotaxis model of Keller-Segel (KS) type with a logistic growth term. Because of its ability to display auto-aggregation, the KS model has been widely…

Biological Physics · Physics 2011-11-14 S. Banerjee , A. P. Misra , L. Rondoni

The phenomenon where cells with elongated protrusions, such as neurons, communicate by contacting other cells and arrange themselves appropriately is termed cell sorting through haptotaxis. This phenomenon is described by partial…

Analysis of PDEs · Mathematics 2026-01-01 Hiroshi Ishii , Hideki Murakawa , Yoshitaro Tanaka

The spreading of bacterial populations is central to processes in agriculture, the environment, and medicine. However, existing models of spreading typically focus on cells in unconfined settings--despite the fact that many bacteria inhabit…

Populations and Evolution · Quantitative Biology 2022-06-07 Daniel B. Amchin , Jenna A. Ott , Tapomoy Bhattacharjee , Sujit S. Datta

It is known that solutions of the parabolic elliptic Keller-Segel equations in the two dimensional plane decay, as time goes to infinity, provided the initial data admits sub-critical mass and finite second moments, while such solution…

Analysis of PDEs · Mathematics 2018-02-27 Debabrata Karmakar , Gershon Wolansky

Derived from a biophysical model for the motion of a crawling cell, the system \[(*)~\begin{cases}u_t=\Delta u-\nabla\cdot(u\nabla v)\\0=\Delta v-kv+u\end{cases}\] is investigated in a finite domain $\Omega\subset\mathbb{R}^n$, $n\geq2$,…

Analysis of PDEs · Mathematics 2021-01-19 Jan Fuhrmann , Johannes Lankeit , Michael Winkler

Chemotaxis plays a crucial role in a variety of processes in biology and ecology. Quite often it acts to improve efficiency of biological reactions; one example is the immune system signalling, where infected tissues release chemokines…

Analysis of PDEs · Mathematics 2025-08-20 Jing An , Alexander Kiselev , Yao Yao

We study the existence of steady states to the Keller-Segel system with linear chemotactical sensitivity function on a smooth bounded domain in $\mathbb R^N,$ $N\ge3,$ having rotational symmetry. We find three different types of…

Analysis of PDEs · Mathematics 2016-03-22 Oscar Agudelo , Angela Pistoia