Keller-Segel chemotaxis models: A review
We recount and discuss some of the most important methods and blow-up criteria for
analyzing solutions of Keller-Segel chemotaxis models. First, we discuss the results …
analyzing solutions of Keller-Segel chemotaxis models. First, we discuss the results …
Positivity-preserving and energy-dissipative finite difference schemes for the Fokker–Planck and Keller–Segel equations
In this work we introduce semi-implicit or implicit finite difference schemes for the continuity
equation with a gradient flow structure. Examples of such equations include the linear …
equation with a gradient flow structure. Examples of such equations include the linear …
Discrete maximum principle of a high order finite difference scheme for a generalized Allen-Cahn equation
We consider solving a generalized Allen-Cahn equation coupled with a passive convection
for a given incompressible velocity field. The numerical scheme consists of the first order …
for a given incompressible velocity field. The numerical scheme consists of the first order …
Error estimates and blow-up analysis of a finite-element approximation for the parabolic-elliptic Keller-Segel system
W Chen, Q Liu, J Shen - arxiv preprint arxiv:2212.07655, 2022 - arxiv.org
The Keller-Segel equations are widely used for describing chemotaxis in biology. Recently,
a new fully discrete scheme for this model was proposed in [46], mass conservation …
a new fully discrete scheme for this model was proposed in [46], mass conservation …
An unconditionally energy stable and positive upwind DG scheme for the Keller–Segel model
The well-suited discretization of the Keller–Segel equations for chemotaxis has become a
very challenging problem due to the convective nature inherent to them. This paper aims to …
very challenging problem due to the convective nature inherent to them. This paper aims to …
Bound-preserving finite element approximations of the Keller–Segel equations
This paper aims to develop numerical approximations of the Keller–Segel equations that
mimic at the discrete level the lower bounds and the energy law of the continuous problem …
mimic at the discrete level the lower bounds and the energy law of the continuous problem …
On a chemotaxis-Navier-Stokes system with Lotka-Volterra competitive kinetics: Theoretical and numerical analysis
This work is devoted to the theoretical and numerical analysis of a two-species chemotaxis-
Navier-Stokes system with Lotka-Volterra competitive kinetics in a bounded domain of R d …
Navier-Stokes system with Lotka-Volterra competitive kinetics in a bounded domain of R d …
Direct discontinuous Galerkin method with interface correction for the Keller-Segel chemotaxis model
Abstract The Keller-Segel (KS) chemotaxis equation is a widely studied mathematical model
for understanding the collective behavior of cells in response to chemical gradients. This …
for understanding the collective behavior of cells in response to chemical gradients. This …
Analysis of a fully discrete approximation for the classical Keller–Segel model: Lower and a priori bounds
JV Gutiérrez-Santacreu… - Computers & Mathematics …, 2021 - Elsevier
This paper is devoted to constructing approximate solutions for the classical Keller–Segel
model governing chemotaxis. It consists of a system of nonlinear parabolic equations, where …
model governing chemotaxis. It consists of a system of nonlinear parabolic equations, where …
A posteriori error control for a Discontinuous Galerkin approximation of a Keller-Segel model
We provide a posteriori error estimates for a discontinuous Galerkin scheme for the
parabolic-elliptic Keller-Segel system in 2 or 3 space dimensions. The estimates are …
parabolic-elliptic Keller-Segel system in 2 or 3 space dimensions. The estimates are …