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Analysis of a Degenerate and Singular Volume-Filling Cross-Diffusion System Modeling Biofilm Growth (CROSBI ID 269122)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Daus, Esther S. ; Milišić, Josipa Pina ; Zamponi, Nicola Analysis of a Degenerate and Singular Volume-Filling Cross-Diffusion System Modeling Biofilm Growth // Siam journal on mathematical analysis, 51 (2019), 4; 3569-3605. doi: 10.1137/18m1185806

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

Povezanost rada

Matematika

Poveznice
Indeksiranost