Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long-time existence of classical solutions to a 1-D swelling gel   In this paper we derived a model which describes the swelling dynamics of a
gel and study the system in one-dimensional geometry with a free boundary. The
governing equations are hyperbolic with a weakly dissipative source. Using a
mass-Lagrangian formulation, the free-boundary is transformed into a
fixed-boundary. We prove the existence of long time, continuously
differentiable solutions to the transformed fixed boundary problem.

22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex