Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and regularity of source-type self-similar solutions for
  stable thin-film equations   We investigate the existence and the boundary regularity of source-type
self-similar solutions to the thin-film equation
$h_t=-(h^nh_{zzz})_z+(h^{n+3})_{zz},$ $ t>0,\; z\in \mathbb{R};\; h(0,z)=
\omega \delta(z)$ where $n\in (\frac{3}{2},3),\; \omega > 0$ and $\delta$ is
the Dirac mass at the origin. It is known that the leading order expansion near
the edge of the support coincides with that of a traveling-wave solution for
the standard thin-film equation: $h_t=-(h^nh_{zzz})_z$. In this paper we
sharpen this result, proving that the higher order corrections are analytic
with respect to three variables: the first one is just the {spatial} variable,
whereas the second and the third (except for $n = 2$) are irrational powers of
it. It is known that this third variable does not appear for the thin-film
equation without gravity.

8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga