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Related papers: A stochastic Keller-Segel model of chemotaxis

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The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on {\em E. coli} have shown precise structure of traveling pulses. We present here an alternative…

In this paper we study the controllability of a coupled Keller-Segel-Navier-Stokes system. We show the local exact controllability of the system around some particular trajectories. The proof relies on new Carleman inequalities for the…

Optimization and Control · Mathematics 2016-03-11 Felipe W. Chaves-Silva , Sergio Guerrero

Kinetic-transport equations that take into account the intra-cellular pathways are now considered as the correct description of bacterial chemotaxis by run and tumble. Recent mathematical studies have shown their interest and their…

Analysis of PDEs · Mathematics 2018-06-13 Benoît Perthame , Weiran Sun , Min Tang

This paper is concerned with a chemotaxis aggregation model for cells, more precisely with a parabolic-elliptic semilinear Patlak-Keller-Segel system in a ball of $\mathbb{R}^N$ for $N\geq 2$. For $N=2$, this system is well known for its…

Analysis of PDEs · Mathematics 2014-06-03 Alexandre Montaru

This paper continues our survey about the mean-field derivation of the two-dimensional signal-dependent Keller-Segel system studied in [1]. Therefore, we consider the same system of moderately interacting particles as before. The difference…

Probability · Mathematics 2026-05-18 Lukas Bol , Li Chen

We show the existence of local and global in time weak martingale solutions for a stochastic version of the Othmer-Dunbar-Alt kinetic model of chemotaxis under suitable assumptions on the turning kernel and stochastic drift coefficients,…

Analysis of PDEs · Mathematics 2026-03-30 Benjamin Gess , Sebastian Herr , Anne Niesdroy

Fluctuating hydrodynamics provides a quantitative, large-scale description of many-body systems in terms of smooth variables, with microscopic details entering only through a small set of transport coefficients. Although this framework has…

Statistical Mechanics · Physics 2026-01-06 Soumyabrata Saha , Sandeep Jangid , Thibaut Arnoulx de Pirey , Juliane U. Klamser , Tridib Sadhu

This paper deals with the homogeneous Neumann boundary-value problem for the Keller--Segel system \begin{align*} \begin{cases} u_t=\Delta u - \chi \nabla \cdot (u|\nabla v|^{p-2}\nabla v),\\[] v_t=\Delta v - v + u^{\theta} \end{cases}…

Analysis of PDEs · Mathematics 2025-01-09 Shohei Kohatsu

In this paper the first equation within a class of well known chemotaxis systems is derived as a hydrodynamic limit from a stochastic interacting many particle system on the lattice. The cells are assumed to interact with attractive…

Probability · Mathematics 2018-04-26 Stefan Grosskinsky , Daniel Marahrens , Angela Stevens

Three-dimensional cultures of cells are gaining popularity as an in vitro improvement over 2D Petri dishes. In many such experiments, cells have been found to organize in aggregates. We present new results of three-dimensional in vitro…

Cell Behavior · Quantitative Biology 2018-11-01 Federica Bubba , Camille Pouchol , Nathalie Ferrand , Guillaume Vidal , Luis Almeida , Benoıt Perthame , Michèle Sabbah

We are concerned with the hyperbolic Keller-Segel model with quorum sensing, a model describing the collective cell movement due to chemical signalling with a flux limitation for high cell densities. This is a first order quasilinear…

Analysis of PDEs · Mathematics 2007-05-23 Benoit Perthame , Anne-Laure Dalibard

This paper is devoted to global existence of weak solutions to the following degenerate kinetic model of chemotaxis \begin{equation} \begin{cases}\label{chemo0} u_t=\Delta (\gamma (v)u) \tau v_{t}=\Delta v-v+u \end{cases} \end{equation}in a…

Analysis of PDEs · Mathematics 2020-07-21 Haixia Li , Jie Jiang

This chapter provides a brief introduction to the theory and practice of spatial stochastic simulations. It begins with an overview of different methods available for biochemical simulations highlighting their strengths and limitations.…

Quantitative Methods · Quantitative Biology 2018-10-02 Sanjana Gupta , Jacob Czech , Robert Kuczewski , Thomas M. Bartol , Terrence J. Sejnowski , Robin E. C. Lee , James R. Faeder

We propose a simple discrete stochastic model for calcium dynamics in living cells. Specifically, the calcium concentration distribution is assumed to give rise to a set of probabilities for the opening/closing of channels which release…

patt-sol · Physics 2009-10-31 Markus Baer , Martin Falcke , Herbert Levine , Lev S. Tsimring

This work is a series of two articles. The main goal is to rigorously derive the degenerate parabolic-elliptic Keller-Segel system in the sub-critical regime from a moderately interacting stochastic particle system. In the first article…

Probability · Mathematics 2026-02-13 Li Chen , Veniamin Gvozdik , Yue Li

In this work we introduce a new optimal control algorithm for the Keller-Segel chemo-attraction system, where both boundary and distributed controls are considered and both are associated with introducing/removing the amount of chemical…

Optimization and Control · Mathematics 2026-03-20 F. Guillen-Gonzalez , F. Palmero-Ramos , M. A. Rodriguez-Bellido , G. Tierra

In this paper, we propose a kinetic model describing the collective motion by chemotaxis of two species in interaction emitting the same chemoattractant. Such model can be seen as a generalisation to several species of the Othmer-Dunbar-Alt…

Analysis of PDEs · Mathematics 2014-04-21 Luís Almeida , Casimir Emako , Nicolas Vauchelet

An optimal control problem associated to the Keller-Segel with logistic reaction system will be studied in $2D$ domains. The control acts in a bilinear form only in the chemical equation. The existence of optimal control and a necessary…

Optimization and Control · Mathematics 2022-07-01 P. Braz e Silva , F. Guillén-González , C. F. Perusato , M. A. Rodríguez-Bellido

The present work deals with a Keller-Segel-Navier-Stokes system with potential consumption, under homogeneous Neumann boundary conditions for cell density and chemical signal, and of Dirichlet type for the velocity field, over a bounded…

Analysis of PDEs · Mathematics 2025-06-24 Daniel Barbosa , Gabriela Planas , Francisco Guillén-González

We consider a model of congestion dynamics with chemotaxis, where the density of cells follows the chemical signal it generates, while observing an incompressibility constraint. We show that when the chemical diffuses slowly and attracts…

Analysis of PDEs · Mathematics 2022-04-27 Inwon Kim , Antoine Mellet , Yijing Wu