Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear stability of viscous roll waves   Extending results of Oh--Zumbrun and Johnson--Zumbrun for parabolic
conservation laws, we show that spectral stability implies nonlinear stability
for spatially periodic viscous roll wave solutions of the one-dimensional St.
Venant equations for shallow water flow down an inclined ramp. The main new
issues to be overcome are incomplete parabolicity and the nonconservative form
of the equations, which leads to undifferentiated quadratic source terms that
cannot be handled using the estimates of the conservative case. The first is
resolved by treating the equations in the more favorable Lagrangian
coordinates, for which one can obtain large-amplitude nonlinear damping
estimates similar to those carried out by Mascia--Zumbrun in the related shock
wave case, assuming only symmetrizability of the hyperbolic part. The second is
resolved by the observation that, similarly as in the relaxation and detonation
cases, sources occurring in nonconservative components experience greater than
expected decay, comparable to that experienced by a differentiated source.

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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph