Positivity-preserving high-order compact difference method for the Keller-Segel chemotaxis model

DOI10.3934/mbe.2022319OpenAlexW4283314487MaRDI QIDQ2686817

Yongbin Ge, Zhi Wang, Lin Zhang

Publication date: 28 February 2023

Published in: Mathematical Biosciences and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/mbe.2022319

zbMATH Keywords

positivity-preservinghigh-order compact difference schemeKeller-Segel chemotaxis modelnonlinear advection diffusion reaction equationnon-constant stationary

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Cell movement (chemotaxis, etc.) (92C17)

Related Items

High-order finite difference approximation of the Keller-Segel model with additional self- and cross-diffusion terms and a logistic source

Uses Software

• Chemotaxis

Cites Work

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• Boundedness in a parabolic-parabolic quasilinear chemotaxis system with logistic source
• Fully discrete analysis of a discontinuous finite element method for the keller-segel chemotaxis model
• Stability of spiky solution of Keller-Segel's minimal chemotaxis model
• Notes on finite difference schemes to a parabolic-elliptic system modelling chemotaxis
• Initiation of slime mold aggregation viewed as an instability
• Model for chemotaxis
• Traveling bands of chemotactic bacteria: a theoretical analysis
• On convergence to equilibria for the Keller-Segel chemotaxis model
• A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models
• A user's guide to PDE models for chemotaxis
• Nonlinear aspects of chemotaxis
• Compact finite difference schemes with spectral-like resolution
• From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
• Local discontinuous Galerkin method for the Keller-Segel chemotaxis model
• High-order positivity-preserving hybrid finite-volume-finite-difference methods for chemotaxis systems
• Finite-time blow-up for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type
• From 1970 until present: the Keller-Segel model in chemotaxis and its consequences. II
• Upwind-difference potentials method for Patlak-Keller-Segel chemotaxis model
• Spiky and transition layer steady states of chemotaxis systems via global bifurcation and Helly's compactness theorem
• New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
• Energy dissipative local discontinuous Galerkin methods for Keller-Segel chemotaxis model
• Keller-Segel chemotaxis models: a review
• Third order positivity-preserving direct discontinuous Galerkin method with interface correction for chemotaxis Keller-Segel equations
• Numerical simulations for the chemotaxis models on surfaces via a novel characteristic finite element method
• A positivity preserving moving mesh finite element method for the Keller-Segel chemotaxis model
• A finite volume scheme for the Patlak-Keller-Segel chemotaxis model
• Compact difference schemes for heat equation with Neumann boundary conditions (II)
• Random walk with persistence and external bias
• Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments
• The one-dimensional chemotaxis model: global existence and asymptotic profile
• Nonoscillatory High Order Accurate Self-Similar Maximum Principle Satisfying Shock Capturing Schemes I
• A Chemotaxis System with Logistic Source
• New Interior Penalty Discontinuous Galerkin Methods for the Keller–Segel Chemotaxis Model
• A mechanochemical model of angiogenesis and vasculogenesis
• Heat transfer at high Péclet number from a small sphere freely rotating in a simple shear field
• Fractional step methods applied to a chemotaxis model