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arXiv · 1805.02106

Analysis of a degenerate and singular volume-filling cross-diffusion system modeling biofilm growth

Esther S. Daus·Josipa-Pina Milišić·Nicola Zamponi
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Abstract

We analyze the mathematical properties of a multi-species 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, which make the analysis extremely challenging. The equations also admit a very interesting non-standard 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.

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Esther S. Daus, Josipa-Pina Milišić, Nicola Zamponi. 2018-05-05. Analysis of a degenerate and singular volume-filling cross-diffusion system modeling biofilm growth. https://arxiv.org/abs/1805.02106

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