by J.W. Barrett, K. Deckelnick.
Series: 2006-25, Preprints
We consider a nonlinear parabolic system which models the
spatiotemporal evolution of a bacterium on a thin film of
nutrient. The nutrient concentration satisfies a reaction
diffusion equation while the equation for the bacterial cell density is of porous medium type. The diffusion coefficient
in that equation also depends in a degenerate way on the nutrient concentration making the system possibly doubly
degenerate. We prove existence and uniqueness of a weak
solution and obtain error bounds for a fully practical
finite element method for the above system.
doubly-degenerate parabolic system, bacterial pattern formation, existence, uniqueness, finite elements, error analysis