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| We analyze a prototype model of the colony of cells forming a biofilm.
The model describes changes in biofilm density caused by nonlinear diffusion, food (nutrients) taxis and cell proliferation. The model is a system of two quasilinear degenerate/singular parabolic equations into which two thresholds are built in. One occurs at zero cell density level, the second one is related to the maximal density which the cells
cannot exceed. Accordingly, both diffusion and taxis terms have degenerate or
singular parts. This model extends a previously introduced degenerate biofillm
model by combining it with the food-taxis. We give conditions for existence and uniqueness of weak global solutions and illustrate the model behavior
in numerical simulations. The results are contained in the joint paper by H.~Eberl, M.~Efendiev, A.Zhigun and D.W. {\it Analysis of a degenerate biofilm model with a nutrient taxis term}, Discrete and Continuous Dynamical Systems 34 (1) 2014. 99-119 |
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