Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global well-posedness and multi-tone solutions of a class of nonlinear
  nonlocal cochlear models in hearing   We study a class of nonlinear nonlocal cochlear models of the transmission
line type, describing the motion of basilar membrane (BM) in the cochlea. They
are damped dispersive partial differential equations (PDEs) driven by time
dependent boundary forcing due to the input sounds. The global well-posedness
in time follows from energy estimates. Uniform bounds of solutions hold in case
of bounded nonlinear damping. When the input sounds are multi-frequency tones,
and the nonlinearity in the PDEs is cubic, we construct smooth quasi-periodic
solutions (multi-tone solutions) in the weakly nonlinear regime, where new
frequencies are generated due to nonlinear interaction. When the input is two
tones at frequencies $f_1$, $f_2$ ($f_1 < f_2$), and high enough intensities,
numerical results illustrate the formation of combination tones at $2 f_1 -f_2$
and $2f_2 -f_1$, in agreement with hearing experiments. We visualize the
frequency content of solutions through the FFT power spectral density of
displacement at selected spatial locations on BM.

8
The categories of this paper are: hep-ex
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int