Naslov
Analysis of a Degenerate and Singular Volume-Filling Cross-Diffusion System Modeling Biofilm Growth

Autori
Daus, Esther S. ; Milišić, Josipa Pina ; Zamponi, Nicola

Izvornik
SIAM Journal on Mathematical Analysis (0036-1410) 51 (2019), 4; 3569-3605

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Biofilm model, volume-filling model, entropy method, global existence of weak solutions, long-time convergence, uniqueness of solutions

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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