Nonnegativity of exact and numerical solutions of some chemotactic models

DOI10.1016/J.CAMWA.2013.05.014zbMath1344.92031OpenAlexW2122409169MaRDI QIDQ305536

Erica Zuhr, Patrick De Leenheer, Jay Gopalakrishnan

Publication date: 30 August 2016

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://pdxscholar.library.pdx.edu/mth_fac/37

zbMATH Keywords

monotonenumerical methodspattern formationblow upKeller-Segelspurious

Mathematics Subject Classification ID

Cell movement (chemotaxis, etc.) (92C17) Positive solutions to PDEs (35B09)

Related Items (11)

Preserving nonnegativity of an affine finite element approximation for a convection-diffusion-reaction problem ⋮ Convergence rate estimates of solutions in a higher dimensional chemotaxis system with logistic source ⋮ A meshless technique based on the local radial basis functions collocation method for solving parabolic-parabolic Patlak-Keller-Segel chemotaxis model ⋮ Analysis of a fully discrete approximation for the classical Keller-Segel model: lower and \textit{a priori} bounds ⋮ Study of a chemo-repulsion model with quadratic production. I: Analysis of the continuous problem and time-discrete numerical schemes ⋮ Finite element numerical schemes for a chemo-attraction and consumption model ⋮ Positive nonlinear DDFV scheme for a degenerate parabolic system describing chemotaxis ⋮ Finite element approximation of a Keller-Segel model with additional self- and cross-diffusion terms and a logistic source ⋮ A new numerical method to solve some \(\mathrm{PDE_s}\) in the unit ball and comparison with the finite element and the exact solution ⋮ A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes ⋮ Comparison of two finite element schemes for a chemo-repulsion system with quadratic production

Uses Software

• Triangle

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generalizing the Keller-Segel model: Lyapunov functionals, steady state analysis, and blow-up results for multi-species chemotaxis models in the presence of attraction and repulsion between competitive interacting species
• Fully discrete analysis of a discontinuous finite element method for the keller-segel chemotaxis model
• A conservative and monotone mixed-hybridized finite element approximation of transport problems in heterogeneous domains
• Efficient, accurate and flexible finite element solvers for chemotaxis problems
• Initiation of slime mold aggregation viewed as an instability
• A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models
• Nonlinear aspects of chemotaxis
• From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
• Error analysis of a conservative finite-element approximation for the Keller-Segel system of chemotaxis
• A flux-corrected finite element method for chemotaxis problems
• An a priori error estimate for a monotone mixed finite-element discretization of a convection-diffusion problem
• Random walk with persistence and external bias
• Instability in a generalized Keller–Segel model
• Conservative upwind finite-element method for a simplified Keller–Segel system modelling chemotaxis
• Inverse-Average-Type Finite Element Discretizations of Selfadjoint Second-Order Elliptic Problems
• Stationary Solutions of Chemotaxis Systems
• On a conservation upwind finite element scheme for convective diffusion equations
• Two-Dimensional Exponential Fitting and Applications to Drift-Diffusion Models
• A monotone finite element scheme for convection-diffusion equations
• New Interior Penalty Discontinuous Galerkin Methods for the Keller–Segel Chemotaxis Model
• EQUILIBRIUM OF TWO POPULATIONS SUBJECT TO CHEMOTAXIS
• Numerical simulation of chemotactic bacteria aggregation via mixed finite elements
• Galerkin Finite Element Methods for Parabolic Problems
• Fractional step methods applied to a chemotaxis model
• The nonsymmetric case of the Keller-Segel model in chemotaxis: some recent results.

This page was built for publication: Nonnegativity of exact and numerical solutions of some chemotactic models