Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Periodic-coefficient damping estimates, and stability of large-amplitude
  roll waves in inclined thin film flow   A technical obstruction preventing the conclusion of nonlinear stability of
large-Froude number roll waves of the St. Venant equations for inclined thin
film flow is the "slope condition" of Johnson-Noble-Zumbrun, used to obtain
pointwise symmetrizability of the linearized equations and thereby
high-frequency resolvent bounds and a crucial H s nonlinear damping estimate.
Numerically, this condition is seen to hold for Froude numbers 2 \textless{} F
3.5, but to fail for 3.5 F. As hydraulic engineering applications typically
involve Froude number 3 F 5, this issue is indeed relevant to practical
considerations. Here, we show that the pointwise slope condition can be
replaced by an averaged version which holds always, thereby completing the
nonlinear theory in the large-F case. The analysis has potentially larger
interest as an extension to the periodic case of a type of weighted
"Kawashima-type" damping estimate introduced in the asymptotically-constant
coefficient case for the study of stability of large-amplitude viscous shock
waves.

22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph