Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long-time stability of large-amplitude noncharacteristic boundary layers
  for hyperbolic--parabolic systems   Extending investigations of Yarahmadian and Zumbrun in the strictly parabolic
case, we study time-asymptotic stability of arbitrary (possibly large)
amplitude noncharacteristic boundary layers of a class of hyperbolic-parabolic
systems including the Navier--Stokes equations of compressible gas- and
magnetohydrodynamics, establishing that linear and nonlinear stability are both
equivalent to an Evans function, or generalized spectral stability, condition.
The latter is readily checkable numerically, and analytically verifiable in
certain favorable cases; in particular, it has been shown by Costanzino,
Humpherys, Nguyen, and Zumbrun to hold for sufficiently large-amplitude layers
for isentropic ideal gas dynamics, with general adiabiatic index $\gamma \ge
1$. Together with these previous results, our results thus give nonlinear
stability of large-amplitude isentropic boundary layers, the first such result
for compressive (``shock-type'') layers in other than the nearly-constant case.
The analysis, as in the strictly parabolic case, proceeds by derivation of
detailed pointwise Green function bounds, with substantial new technical
difficulties associated with the more singular, hyperbolic behavior in the
high-frequency/short time regime.

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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph