Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of a degenerate and singular volume-filling cross-diffusion
  system modeling biofilm growth   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.

14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int