Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bound-Preserving Finite-Volume Schemes for Systems of Continuity
  Equations with Saturation   We propose finite-volume schemes for general continuity equations which
preserve positivity and global bounds that arise from saturation effects in the
mobility function. In the case of gradient flows, the schemes dissipate the
free energy at the fully discrete level. Moreover, these schemes are
generalised to coupled systems of non-linear continuity equations, such as
multispecies models in mathematical physics or biology, preserving the bounds
and the dissipation of the energy whenever applicable. These results are
illustrated through extensive numerical simulations which explore known
behaviours in biology and showcase new phenomena not yet described by the
literature.

3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn