06-25
Existence, uniqueness and approximation of a doubly-degenerate nonlinear parabolic system
by J.W. Barrett; K. Deckelnick
Preprint series: 06-25, Preprints
- MSC:
- 35K65 Parabolic partial differential equations of degenerate type
- 35K55 Nonlinear PDE of parabolic type
- 65M15 Error bounds
- 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Abstract: 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.
Keywords: doubly-degenerate parabolic system, bacterial pattern formation, existence, uniqueness, finite elements, error analysis
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