Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long time asymptotics for homoenergetic solutions of the Boltzmann
  equation. Hyperbolic-dominated case   In this paper we continue the formal analysis of the long-time asymptotics of
the homoenergetic solutions for the Boltzmann equation that we began in [18].
They have the form $f\left( x,v,t\right) =g\left(v-L\left( t\right) x,t\right)
$ where $L\left( t\right) =A\left(I+tA\right) ^{-1}$ where $A$ is a constant
matrix. Homoenergetic solutions satisfy an integro-differential equation which
contains, in addition to the classical Boltzmann collision operator, a linear
hyperbolic term. Depending on the properties of the collision kernel the
collision and the hyperbolic terms might be of the same order of magnitude as
$t\to\infty$, or the collision term could be the dominant one for large times,
or the hyperbolic term could be the largest. The first case has been rigorously
studied in [17]. Formal asymptotic expansions in the second case have been
obtained in [18]. All the solutions obtained in this case can be approximated
by Maxwellian distributions with changing temperature. In this paper we focus
in the case where the hyperbolic terms are much larger than the collision term
for large times (hyperbolic-dominated behavior). In the hyperbolic-dominated
case it does not seem to be possible to describe in a simple way all the long
time asymptotics of the solutions, but we discuss several physical situations
and formulate precise conjectures. We give explicit formulas for the
relationship between density, temperature and entropy for these solutions.
These formulas differ greatly from the ones at equilibrium.

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The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con