Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the geometry of the domain of the solution of nonlinear Cauchy
  problem   We consider the Cauchy problem for a second order quasi-linear partial
differential equation with an admissible parabolic degeneration such that the
given functions described the initial conditions are defined on a closed
interval. We study also a variant of the inverse problem of the Cauchy problem
and prove that the considered inverse problem has a solution under certain
regularity condition. We illustrate the Cauchy and the inverse problems in some
interesting examples such that the families of the characteristic curves have
either common envelopes or singular points. In these cases the definition
domain of the solution of the differential equation contains a gap.

34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int