Analysis of a Degenerate and Singular Volume-Filling Cross-Diffusion System Modeling Biofilm Growth (CROSBI ID 269122)
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Podaci o odgovornosti
Daus, Esther S. ; Milišić, Josipa Pina ; Zamponi, Nicola
engleski
Analysis of a Degenerate and Singular Volume-Filling Cross-Diffusion System Modeling Biofilm Growth
We analyze the mathematical properties of a multispecies biofilm cross-diffusion model together with very general reaction terms and mixed Dirichlet--Neumann boundary conditions on a bounded domain. This model belongs to the class of volume-filling-type cross-diffusion systems which exhibit a porous medium--type degeneracy when the total biomass vanishes as well as a superdiffusion-type singularity when the biomass reaches its maximum cell capacity. The equations also admit a very interesting nonstandard entropy structure. We prove the existence of global-in-time weak solutions, study the asymptotic behavior and the uniqueness of the solutions, and complement the analysis by numerical simulations that illustrate the theoretically obtained results.
Biofilm model, volume-filling model, entropy method, global existence of weak solutions, long-time convergence, uniqueness of solutions
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Podaci o izdanju
51 (4)
2019.
3569-3605
objavljeno
0036-1410
1095-7154
10.1137/18m1185806