Global well-posedness and multi-tone solutions of a class of nonlinear nonlocal cochlear models in hearing

Jack Xin Yingyong Qi

Data Analysis mathscidoc:1912.43892

Nonlinearity, 17, (2), 711, 2004.1
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 the 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 consists of 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 2f 1 f 2 and 2f 2 f 1, in agreement with hearing experiments. We visualize
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@inproceedings{jack2004global,
  title={Global well-posedness and multi-tone solutions of a class of nonlinear nonlocal cochlear models in hearing},
  author={Jack Xin, and Yingyong Qi},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210501696722456},
  booktitle={Nonlinearity},
  volume={17},
  number={2},
  pages={711},
  year={2004},
}
Jack Xin, and Yingyong Qi. Global well-posedness and multi-tone solutions of a class of nonlinear nonlocal cochlear models in hearing. 2004. Vol. 17. In Nonlinearity. pp.711. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210501696722456.
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