Nonlinear flux-limited models for chemotaxis on networks

DOI10.3934/nhm.2017017zbMath1376.92011OpenAlexW2753918982MaRDI QIDQ1680941

T. N. Ha Pham, Axel Klar, Raul Borsche

Publication date: 17 November 2017

Published in: Networks and Heterogeneous Media (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/nhm.2017017

zbMATH Keywords

moment closurenetworkschemotaxiskinetic equationrelaxation schemescoupling conditionsnonlinear maximum entropy

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Cell movement (chemotaxis, etc.) (92C17) Systems biology, networks (92C42)

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Uses Software

• Chemotaxis

Cites Work

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• On a chemotaxis model with saturated chemotactic flux
• Asymptotic-preserving and well-balanced schemes for the 1D Cattaneo model of chemotaxis movement in both hyperbolic and diffusive regimes
• Derivation of hyperbolic models for chemosensitive movement
• Initiation of slime mold aggregation viewed as an instability
• Model for chemotaxis
• Volume effects in the Keller--Segel model: energy estimates preventing blow-up
• An asymptotic preserving relaxation scheme for a moment model of radiative transfer
• Half-moment closure for radiative transfer equations
• A user's guide to PDE models for chemotaxis
• Nonlinear aspects of chemotaxis
• Finite time blow-up in some models of chemotaxis
• An asymptotic-preserving well-balanced scheme for the hyperbolic heat equations
• Asymptotic preserving scheme and numerical methods for radiative hydrodynamic models
• Kinetic models for chemotaxis and their drift-diffusion limits
• Analysis of the \(M 1\) model: well-posedness and diffusion asymptotics
• Parabolic models for chemotaxis on weighted networks
• Localization effects and measure source terms in numerical schemes for balance laws
• Kinetic and related macroscopic models for chemotaxis on networks
• THE SCALAR KELLER–SEGEL MODEL ON NETWORKS
• ON THE ASYMPTOTIC THEORY FROM MICROSCOPIC TO MACROSCOPIC GROWING TISSUE MODELS: AN OVERVIEW WITH PERSPECTIVES
• Higher Order Mixed-Moment Approximations for the Fokker--Planck Equation in One Space Dimension
• A Macro-kinetic Hybrid Model for Traffic Flow on Road Networks
• Global Smooth Solutions for a Hyperbolic Chemotaxis Model on a Network
• The one-dimensional Keller–Segel model with fractional diffusion of cells
• MULTISCALE BIOLOGICAL TISSUE MODELS AND FLUX-LIMITED CHEMOTAXIS FOR MULTICELLULAR GROWING SYSTEMS
• Diffusive Relaxation Schemes for Multiscale Discrete-Velocity Kinetic Equations
• HYPERBOLIC MODELS FOR CHEMOSENSITIVE MOVEMENT
• The relaxation schemes for systems of conservation laws in arbitrary space dimensions
• A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations
• A fully-discrete-state kinetic theory approach to traffic flow on road networks
• Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
• A hyperbolic model of chemotaxis on a network: a numerical study

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