Reduced equations for an active model of the hydroelastic waves in the cochlea

2020/08/10 by Rubinstein, Jacob, Sternberg, Peter
#92-10 (primary) 35B40 (secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2008.04343

Abstract

Building upon our earlier passive models for the cochlea, here we enhance the model with an active mechanism. Starting with a one-chamber simplification leading to a system of a time-dependent PDE in two spatial variables for the pressure coupled to a PDE in one spatial variable for the oscillation of the basilar membrane, we rigorously establish the validity of a dimension reduction to a system to two ODE's. We then present numerical simulations demonstrating the ability of this reduced active system to distinguish and amplify multi-frequency input signals.

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