Kinetic and related macroscopic models for chemotaxis on networks

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

(2015) Luisa Fermo et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

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

A hyperbolic model of chemotaxis on a network: a numerical study

(2013) G. Bretti et al.   ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE

A well-balanced scheme for kinetic models of chemotaxis derived from one-dimensional local forward–backward problems

(2013) Laurent Gosse   MATHEMATICAL BIOSCIENCES

THE SCALAR KELLER–SEGEL MODEL ON NETWORKS

(2013) R. BORSCHE et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

An Asymptotic Preserving Scheme for the Diffusive Limit of Kinetic Systems for Chemotaxis

(2013) José A. Carrillo et al.   MULTISCALE MODELING & SIMULATION

A Macro-kinetic Hybrid Model for Traffic Flow on Road Networks

(2013) M. Herty et al.   Computational Methods in Applied Mathematics

On a chemotaxis model with saturated chemotactic flux

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

Asymptotic High Order Mass-Preserving Schemes for a Hyperbolic Model of Chemotaxis

(2012) R. Natalini et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Asymptotic-Preserving and Well-Balanced schemes for the 1D Cattaneo model of chemotaxis movement in both hyperbolic and diffusive regimes

(2011) Laurent Gosse   JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ON THE ASYMPTOTIC THEORY FROM MICROSCOPIC TO MACROSCOPIC GROWING TISSUE MODELS: AN OVERVIEW WITH PERSPECTIVES

(2011) N. BELLOMO et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

MULTISCALE BIOLOGICAL TISSUE MODELS AND FLUX-LIMITED CHEMOTAXIS FOR MULTICELLULAR GROWING SYSTEMS

(2010) NICOLA BELLOMO et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

The one-dimensional Keller–Segel model with fractional diffusion of cells

(2010) Nikolaos Bournaveas et al.   NONLINEARITY

On general balance laws with boundary

(2009) Rinaldo M. Colombo et al.   JOURNAL OF DIFFERENTIAL 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

On the Cauchy Problem for the p-System at a Junction

(2008) Rinaldo M. Colombo et al.   SIAM JOURNAL ON MATHEMATICAL ANALYSIS