Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Slow motion of internal shock layers for the Jin-Xin system in one space
  dimension   This paper considers the slow motion of the shock layer exhibited by the
solution to the initial-boundary value problem for a scalar hyperbolic system
with relaxation. Such behavior, known as metastable dynamics, is related to the
presence of a first small eigenvalue for the linearized operator around an
equilibrium state; as a consequence, the time-dependent solution approaches its
steady state in an asymptotically exponentially long time interval. In this
contest, both rigorous and asymptotic approaches are used to analyze such slow
motion for the Jin-Xin system. To describe this dynamics we derive an ODE for
the the position of the internal transition layer, proving how it drifts
towards the equilibrium location with a speed rate that is exponentially slow.
These analytical results are also validated by numerical computations.

35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex