Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic behavior of smooth solutions for partially dissipative
  hyperbolic systems with a convex entropy   We study the asymptotic time behavior of global smooth solutions to general
entropy dissipative hyperbolic systems of balance law in m space dimensions,
under the Shizuta-Kawashima condition. We show that these solutions approach
constant equilibrium state in the Lp-norm at a rate O(t^(-m/2(1-1/p))), as t
tends to $\infty$, for p in [min (m,2),+ \infty]. Moreover, we can show that we
can approximate, with a faster order of convergence, theconservative part of
the solution in terms of the linearized hyperbolic operator for m >= 2, and by
a parabolic equation in the spirit of Chapman-Enskog expansion. The main tool
is given by a detailed analysis of the Green function for the linearized
problem.

19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs