Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyperbolic Boundary Value Problems for Symmetric Systems with Variable
  Multiplicities   We extend the Kreiss--Majda theory of stability of hyperbolic
initial--boundary-value and shock problems to a class of systems, notably
including the equations of magnetohydrodynamics (MHD), for which Majda's block
structure condition does not hold: namely, simultaneously symmetrizable systems
with characteristics of variable multiplicity, satisfying at points of variable
multiplicity either a ``totally nonglancing'' or a ``nonglancing and linearly
splitting'' condition. At the same time, we give a simple characterization of
the block structure condition as ``geometric regularity'' of characteristics,
defined as analyticity of associated eigenprojections. The totally nonglancing
or nonglancing and linearly splitting conditions are generically satisfied in
the simplest case of crossings of two characteristics, and likewise for our
main physical examples of MHD or Maxwell equations for a crystal. Together with
previous analyses of spectral stability carried out by Gardner--Kruskal and
Blokhin--Trakhinin, this yields immediately a number of new results of
nonlinear inviscid stability of shock waves in MHD in the cases of parallel or
transverse magnetic field, and recovers the sole previous nonlinear result,
obtained by Blokhin--Trakhinin by direct ``dissipative integral'' methods, of
stability in the zero-magnetic field limit. Our methods apply also to the
viscous case.

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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci