Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structural stability of shock waves in 2D compressible elastodynamics   We study the two-dimensional structural stability of shock waves in a
compressible isentropic inviscid elastic fluid in the sense of the
local-in-time existence and uniqueness of discontinuous shock front solutions
of the equations of compressible elastodynamics in two space dimensions. By the
energy method based on a symmetrization of the wave equation and giving an a
priori estimate without loss of derivatives for solutions of the constant
coefficients linearized problem we find a condition sufficient for the uniform
stability of rectilinear shock waves. Comparing this condition with that for
the uniform stability of shock waves in isentropic gas dynamics, we make the
conclusion that the elastic force plays stabilizing role. In particular, we
show that, as in isentropic gas dynamics, all compressive shock waves are
uniformly stable for convex equations of state. Moreover, for some particular
deformations (and general equations of state), by the direct test of the
uniform Kreiss-Lopatinski condition we show that the stability condition found
by the energy method is not only sufficient but also necessary for uniform
stability. As is known, uniform stability implies structural stability of
corresponding curved shock waves.

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The categories of this paper are: astro-ph
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph