Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

N Bellomo, A Bellouquid, Y Tao… - Mathematical Models and …, 2015 - World Scientific
This paper proposes a survey and critical analysis focused on a variety of chemotaxis
models in biology, namely the classical Keller–Segel model and its subsequent …

On the interplay between mathematics and biology: Hallmarks toward a new systems biology

N Bellomo, A Elaiw, AM Althiabi, MA Alghamdi - Physics of life reviews, 2015 - Elsevier
This paper proposes a critical analysis of the existing literature on mathematical tools
developed toward systems biology approaches and, out of this overview, develops a new …

From a multiscale derivation of nonlinear cross-diffusion models to Keller–Segel models in a Navier–Stokes fluid

N Bellomo, A Bellouquid, N Chouhad - Mathematical Models and …, 2016 - World Scientific
This paper deals with a micro–macro derivation of a variety of cross-diffusion models for a
large system of active particles. Some of the models at the macroscopic scale can be viewed …

[图书][B] Active Particles, Volume 1: Advances in Theory, Models, and Applications

N Bellomo, P Degond, E Tadmor - 2017 - books.google.com
This volume collects ten surveys on the modeling, simulation, and applications of active
particles using methods ranging from mathematical kinetic theory to nonequilibrium …

Learning dynamics towards modeling living systems: Reply to comments on “Collective learning modeling based on the kinetic theory of active particles”

D Burini, S De Lillo, L Gibelli - Physics of Life Reviews, 2016 - Elsevier
Our paper [19] presents a review and critical analysis on a mathematical theory of learning
in populations composed of many interacting individuals. Furthermore, it attempts to provide …

A fully-discrete-state kinetic theory approach to traffic flow on road networks

L Fermo, A Tosin - Mathematical Models and Methods in Applied …, 2015 - World Scientific
This paper presents a new approach to the modeling of vehicular traffic flows on road
networks based on kinetic equations. While in the literature the problem has been …

Asymptotic state lumping in transport and diffusion problems on networks with applications to population problems

J Banasiak, A Falkiewicz… - Mathematical Models and …, 2016 - World Scientific
In this paper we consider a general macro-model describing a metapopulation consisting of
several interacting with each other subpopulations connected through a network, with the …

Mass-preserving approximation of a chemotaxis multi-domain transmission model for microfluidic chips

EC Braun, G Bretti, R Natalini - Mathematics, 2021 - mdpi.com
The present work is inspired by the recent developments in laboratory experiments made on
chips, where the culturing of multiple cell species was possible. The model is based on …

Weakness and mittag–leffler stability of solutions for time-fractional keller–segel models

Y Zhou, J Manimaran, L Shangerganesh… - International Journal of …, 2018 - degruyter.com
We introduce a time-fractional Keller–Segel model with Dirichlet conditions on the boundary
and Caputo fractional derivative for the time. The main result shows the existence theorem of …

[HTML][HTML] Parabolic models for chemotaxis on weighted networks

F Camilli, L Corrias - Journal de Mathematiques Pures et Appliquees, 2017 - Elsevier
In this article we consider the Keller–Segel model for chemotaxis on networks, both in the
doubly parabolic case and in the parabolic–elliptic one. Introducing appropriate transition …