Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approach to steady state in the heat equation and the hyperbolic heat
  transfer equation   We investigate the spherically symmetric 1D ablation problem. We show that
the parabolic heat equation fails to describe the approach to steady state in
infinite space. The hyperbolic equation shows an approach to steady state with
a time constant given by the thermal relaxation time. However the infinite
geometry is rather unphysical and gives rise to a so-called zero mode.
Therefore we also consider the finite problem with a large boundary at constant
temperature. Then both equations show approach to steady state, but only the
hyperbolic equation seems to be physically correct for small times.

20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph