Analysis and Simulations of Coupled Bulk-surface Reaction-Diffusion Systems on Exponentially Evolving Volumes

DOI10.1051/MMNP/201611502zbMath1458.35412OpenAlexW2559873436MaRDI QIDQ4607522

A. H. Chung, Anotida Madzvamuse

Publication date: 14 March 2018

Published in: Mathematical Modelling of Natural Phenomena (Search for Journal in Brave)

Full work available at URL: http://sro.sussex.ac.uk/id/eprint/65941/1/Manuscript_repository.pdf

zbMATH Keywords

diffusion-driven instabilityevolving domainsvolumes and surfacesbulk-surface finite element methodcoupled bulk-surface reaction-diffusion systemsfractional-step \(\theta\) method

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) PDEs in connection with classical thermodynamics and heat transfer (35Q79) Initial-boundary value problems for second-order parabolic systems (35K51) Pattern formations in context of PDEs (35B36)

Related Items (3)

Preface. Bifurcations and Pattern Formation in Biological Applications ⋮ Global existence of solutions to reaction diffusion systems with mass transport type boundary conditions on an evolving domain ⋮ A coupled bulk-surface model for cell polarisation

Uses Software

• deal.ii

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fully implicit time-stepping schemes and non-linear solvers for systems of reaction-diffusion equations
• The \texttt{deal.II} library, version 8.4
• Characterization of Turing diffusion-driven instability on evolving domains
• Stability analysis of non-autonomous reaction-diffusion systems: The effects of growing domains
• The surface finite element method for pattern formation on evolving biological surfaces
• Global existence for semilinear reaction-diffusion systems on evolving domains
• Turing instabilities in a mathematical model for signaling networks
• A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds: application to a model of cell migration and chemotaxis
• Stability analysis of reaction-diffusion models on evolving domains: the effects of cross-diffusion
• Mathematical biology. Vol. 2: Spatial models and biomedical applications.
• Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations
• Kinetics of proton diffusion in the regimes of fast and slow exchange between the membrane surface and the bulk solution
• Reaction-diffusion patterns in plant tip morphogenesis: bifurcations on spherical caps
• Diffusion on a curved surface coupled to diffusion in the volume: application to cell biology
• Implicit--Explicit Timestepping with Finite Element Approximation of Reaction--Diffusion Systems on Evolving Domains
• The Stability of Localized Spot Patterns for the Brusselator on the Sphere
• Symmetry breaking in a bulk–surface reaction–diffusion model for signalling networks
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• The chemical basis of morphogenesis
• Finite element analysis for a coupled bulk-surface partial differential equation
• Projected Finite Elements for Systems of Reaction-Diffusion Equations on Closed Evolving Spheroidal Surfaces
• Simple computation of reaction–diffusion processes on point clouds
• Bulk-mediated Surface Diffusion on a Cylinder in the Fast Exchange Limit
• Stability analysis and simulations of coupled bulk-surface reaction–diffusion systems

This page was built for publication: Analysis and Simulations of Coupled Bulk-surface Reaction-Diffusion Systems on Exponentially Evolving Volumes