Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic stability of planar stationary solution to a 2D
  hyperbolic-elliptic coupled system of the radiating gas in half space   This paper is concerned with the asymptotic stability of planar stationary
solution to an initial-boundary value problem for a two-dimensional
hyperbolic-elliptic coupled system of the radiating gas in half space. We show
that the solution to the problem converges to the corresponding planar
stationary solution as time tends to infinity under small initial perturbation.
These results are proved by the standard $L^2$-energy method. Moreover, we
prove that the solution $(u,q)$ converges to the corresponding planar
stationary solution at the rate $t^{-\alpha/2-1/4}$ for non-degenerate case,
and $t^{-1/4}$ for degenerate case. The proof is based on the time and space
weighted energy method.

33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
19
The categories of this paper are: eess
3
The categories of this paper are: physics
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg