Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entropy conditions for quasilinear first order equations on nonlinear
  fiber bundles with special emphasis on the equation of 2D flat projective
  structure. I   Taking only the characteristics as absolute, in the spirit of Arnold's
"Geometrical Methods in the Theory of Ordinary Differential Equations"
(Springer, 1988), we give an independent of coordinates formulation of general
variational entropy inequalities for quasilinear equations of first order, that
locally read as Kruzhkov inequalities, in terms of certain "entropy densities",
and in the case of the equation of 2D flat projective structure we get the
expression of the general entropy density from its abstract Rankine-Hugoniot
rule for shocks using the projective geometry of the plane.

11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con