Finite element approximation of a Keller–Segel model with additional self- and cross-diffusion terms and a logistic source

Analysis of a fully discrete approximation for the classical Keller–Segel model: Lower and a priori bounds

(2021) Juan Vicente Gutiérrez-Santacreu et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Finite element analysis of a Keller–Segel model with additional cross-diffusion and logistic source. Part I: Space convergence

(2021) Mohammed H. Hashim et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Chemotaxis on networks: Analysis and numerical approximation

(2020) Herbert Egger et al.   ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE

Generalized moving least squares approximation for the solution of local and non-local models of cancer cell invasion of tissue under the effect of adhesion in one- and two-dimensional spaces

(2020) Vahid Mohammadi et al.   COMPUTERS IN BIOLOGY AND MEDICINE

Solving a chemotaxis–haptotaxis system in 2D using Generalized Finite Difference Method

(2020) J.J. Benito et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Positive nonlinear DDFV scheme for a degenerate parabolic system describing chemotaxis

(2020) Moustafa Ibrahim et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

A space time conservation element and solution element method for solving two-species chemotaxis model

(2020) Attia Rabbani et al.   MATHEMATICS AND COMPUTERS IN SIMULATION

Efficient Numerical Algorithms Based on Difference Potentials for Chemotaxis Systems in 3D

(2019) Yekaterina Epshteyn et al.   JOURNAL OF SCIENTIFIC COMPUTING

Adaptive moving mesh upwind scheme for the two-species chemotaxis model

(2019) Alina Chertock et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

On finite volume discretization of infiltration dynamics in tumor growth models

(2019) Xianyi Zeng et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

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

(2015) N. Bellomo et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Nonnegativity of exact and numerical solutions of some chemotactic models

(2013) Patrick De Leenheer et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

On a chemotaxis model with saturated chemotactic flux

(2012) Alina Chertock et al.   Kinetic and Related Models

CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL

(2012) JOSÉ ANTONIO CARRILLO et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Error analysis of a conservative finite-element approximation for the Keller-Segel system of chemotaxis

(2011) Norikazu Saito   COMMUNICATIONS ON PURE AND APPLIED ANALYSIS

Cross Diffusion Preventing Blow-Up in the Two-Dimensional Keller–Segel Model

(2011) Sabine Hittmeir et al.   SIAM JOURNAL ON MATHEMATICAL ANALYSIS

Pattern formation (I): The Keller–Segel model

(2010) Yan Guo et al.   JOURNAL OF DIFFERENTIAL EQUATIONS

Blowup of solutions to generalized Keller–Segel model

(2009) Piotr Biler et al.   JOURNAL OF EVOLUTION EQUATIONS

A user’s guide to PDE models for chemotaxis

(2008) T. Hillen et al.   JOURNAL OF MATHEMATICAL BIOLOGY

A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models

(2008) Alina Chertock et al.   NUMERISCHE MATHEMATIK