2018/05/05 by Esther S. Daus, Daus, Esther S., Josipa‐Pina Milišić +3
Mathematics · Medicine · #Stochastic processes and statistical mechanics #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.1805.02106
We analyze the mathematical properties of a multi-species biofilm\ncross-diffusion model together with very general reaction terms and mixed\nDirichlet-Neumann boundary conditions on a bounded domain. This model belongs\nto the class of volume-filling type cross-diffusion systems which exhibit a\nporous medium-type degeneracy when the total biomass vanishes as well as a\nsuperdiffusion-type singularity when the biomass reaches its maximum cell\ncapacity, which make the analysis extremely challenging. The equations also\nadmit a very interesting non-standard entropy structure. We prove the existence\nof global-in-time weak solutions, study the asymptotic behavior and the\nuniqueness of the solutions, and complement the analysis by numerical\nsimulations that illustrate the theoretically obtained results.\n