Finite element analysis of a Keller-Segel model with additional cross-diffusion and logistic source. II: Time convergence and numerical simulation

DOI10.1016/j.camwa.2022.01.030OpenAlexW4210634305WikidataQ112880460 ScholiaQ112880460MaRDI QIDQ2667976

Akil J. Harfash, Mohammed H. Hashim

Publication date: 2 March 2022

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2022.01.030

zbMATH Keywords

convergenceweak solutionfinite elementchemotaxisKeller-Segel model

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Statistical mechanics of polymers (82D60) Navier-Stokes equations (35Q30) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Cell movement (chemotaxis, etc.) (92C17)

Related Items (4)

Finite element analysis of chemotaxis-growth model with indirect attractant production and logistic source ⋮ Finite element analysis of the two-competing-species Keller-Segel chemotaxis model ⋮ Finite element analysis of nonlinear reaction-diffusion system of Fitzhugh-Nagumo type with Robin boundary conditions ⋮ Finite element analysis of a two-species chemotaxis system with two chemicals

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a chemotaxis model with saturated chemotactic flux
• Initiation of slime mold aggregation viewed as an instability
• PDE models for chemotactic movements: parabolic, hyperbolic and kinetic.
• Nonnegativity preserving convergent schemes for the thin film equation
• Existence of global weak solutions to finitely extensible nonlinear bead-spring chain models for dilute polymers with variable density and viscosity
• Finite element analysis of a Keller-Segel model with additional cross-diffusion and logistic source. I: Space convergence
• Finite element approximation of finitely extensible nonlinear elastic dumbbell models for dilute polymers
• EXISTENCE AND EQUILIBRATION OF GLOBAL WEAK SOLUTIONS TO KINETIC MODELS FOR DILUTE POLYMERS II: HOOKEAN-TYPE MODELS
• Random walk with persistence and external bias
• EXISTENCE AND EQUILIBRATION OF GLOBAL WEAK SOLUTIONS TO KINETIC MODELS FOR DILUTE POLYMERS I: FINITELY EXTENSIBLE NONLINEAR BEAD-SPRING CHAINS
• Cross Diffusion Preventing Blow-Up in the Two-Dimensional Keller–Segel Model
• Existence of Global Weak Solutions to Some Regularized Kinetic Models for Dilute Polymers
• EXISTENCE OF GLOBAL WEAK SOLUTIONS TO DUMBBELL MODELS FOR DILUTE POLYMERS WITH MICROSCOPIC CUT-OFF
• The Derivation of Chemotaxis Equations as Limit Dynamics of Moderately Interacting Stochastic Many-Particle Systems
• CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL
• EXISTENCE OF GLOBAL WEAK SOLUTIONS FOR SOME POLYMERIC FLOW MODELS
• A finite volume scheme for a Keller-Segel model with additional cross-diffusion
• Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains

This page was built for publication: Finite element analysis of a Keller-Segel model with additional cross-diffusion and logistic source. II: Time convergence and numerical simulation