Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Well-posedness of the Cauchy problem for a fourth-order thin film
  equation via regularization approaches   This paper is devoted to some aspects of well-posedness of the Cauchy problem
for a quasilinear degenerate fourth-order parabolic thin film equation u_{t} =
-\nabla \cdot(|u|^{n} \nabla\D u) in \ren \times \re_+, \quad u(x,0)=u_0(x) in
\ren, where $n>0$ is a fixed exponent, with bounded smooth compactly supported
initial data. Dealing with the CP (for, at least, $n \in (0, \frac 32)$)
requires introducing classes of infinitely changing sign solutions that are
oscillatory close to finite interfaces.
  The main goal of the paper is to detect proper solutions of the CP for the
degenerate TFE--4 by uniformly parabolic analytic $\e$-regularizations at least
for values of the parameter $n$ sufficiently close to 0.

34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con