An Effective Model for Biofilm Growth Made by Chemotactical Bacteria in Evolving Porous Media

DOI10.1137/16M108817XzbMath1371.76142OpenAlexW2757091633MaRDI QIDQ5359401

Peter Knabner, Raphael Schulz

Publication date: 25 September 2017

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/16m108817x

zbMATH Keywords

chemotaxisporous mediaparabolic PDEbiofilm growthfluid-solid interactionsevolving microstructure

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Effective constitutive equations in solid mechanics (74Q15) Flows in porous media; filtration; seepage (76S05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Biological fluid mechanics (76Zxx)

Related Items

Homogenisation problems in reactive decontamination, Degenerate equations in a diffusion–precipitation model for clogging porous media, Elliptic equations with discontinuous coefficients in generalized Morrey spaces, Biofilm modeling in evolving porous media with Beavers‐Joseph condition, Numerical investigation of a fully coupled micro-macro model for mineral dissolution and precipitation, Degenerate equations for flow and transport in clogging porous media, Homogenization of a locally periodic time-dependent domain, Analysis of a Degenerate and Singular Volume-Filling Cross-Diffusion System Modeling Biofilm Growth, From Life-Saving to Life-Threatening: A Mathematical Model to Simulate Bacterial Infections in Surgical Procedures, BOUNDEDNESS IN A BIOFILM-CHEMOTAXIS MODEL IN EVOLVING POROUS MEDIA, UNIQUENESS OF DEGENERATING SOLUTIONS TO A DIFFUSION-PRECIPITATION MODEL FOR CLOGGING POROUS MEDIA

Cites Work

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• Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system
• Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion
• A coupled chemotaxis-fluid model: global existence
• On the well posedness of a class of PDEs including porous medium and chemotaxis effect
• Numerical simulation of multi-species biofilms in porous media for different kinetics
• Parabolic equations with BMO coefficients in Lipschitz domains
• Degree theory of BMO. I: Compact manifolds without boundaries
• Existence of smooth solutions to coupled chemotaxis-fluid equations
• Overview of mathematical approaches used to model bacterial chemotaxis. II: Bacterial popu\-lations
• Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
• On the equations rot\ v\(=g\) and div\ u\(=f\) with zero boundary conditions
• Finger Formation in Biofilm Layers
• Corrector estimates for the homogenization of a locally periodic medium with areas of low and high diffusivity
• Homogenisation of a locally periodic medium with areas of low and high diffusivity
• Crystal Precipitation and Dissolution in a Porous Medium: Effective Equations and Numerical Experiments
• Remarks on Global Solvability of 2-D Boussinesq Equations with Non-Decaying Initial Data
• COUPLED CHEMOTAXIS FLUID MODEL
• Strong solvability up to clogging of an effective diffusion–precipitation model in an evolving porous medium
• Analysis of a Two-Scale Phase Field Model for Liquid-Solid Phase Transitions with Equiaxed Dendritic Microstructure
• Global Solutions to the Coupled Chemotaxis-Fluid Equations
• Derivation and analysis of an effective model for biofilm growth in evolving porous media
• Drug release from collagen matrices including an evolving microstructure