EXISTENCE, UNIQUENESS AND APPROXIMATION OF A DOUBLY-DEGENERATE NONLINEAR PARABOLIC SYSTEM MODELLING BACTERIAL EVOLUTION

DOI10.1142/S0218202507002212zbMath1144.35026MaRDI QIDQ5386901

John W. Barrett, Klaus Deckelnick

Publication date: 14 May 2008

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

porous medium equationbacterial pattern formationnonnegative initial datano flux boundary conditions

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Degenerate parabolic equations (35K65) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (6)

Convergence analysis for a nonlinear system of parabolic variational inequalities ⋮ Error analysis of a finite element approximation of a degenerate Cahn-Hilliard equation ⋮ Numerical analysis of a parabolic variational inequality system modeling biofilm growth at the porescale ⋮ Regularity and uniqueness in quasilinear parabolic systems. ⋮ REGULARIZATION SCHEMES FOR DEGENERATE RICHARDS EQUATIONS AND OUTFLOW CONDITIONS ⋮ Finite traveling wave solutions in a degenerate cross-diffusion model for bacterial colony with volume filling

Cites Work

• Unnamed Item
• Compact sets in the space \(L^ p(0,T;B)\)
• Reaction–diffusion modelling of bacterial colony patterns
• Error Analysis of the Enthalpy Method for the Stefan Problem
• Approximation of Degenerate Parabolic Problems Using Numerical Integration
• Weakly Differentiable Functions
• Finite element approximation of a Stefan problem with degenerate Joule heating

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