Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructive Approach of the Solution of Riemann Problem for Shallow
  Water Equations with Topography and Vegetation   We investigate the Riemann Problem for a shallow water model with porosity
and terrain data. Based on recent results on the local existence, we build the
solution in the large settings (the magnitude of the jump in the initial data
is not supposed to be ``small enough''). One difficulty for the extended
solution arises from the double degeneracy of the hyperbolic system describing
the model. Another difficulty is given by the fact that the construction of the
solution assumes solving an equation which has no global solution. Finally, we
present some cases to illustrate the existence and non-existence of the
solution.

13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph