Controllability of a basic cochlea model

Scott W. Hansen

doi:10.3934/eect.2016015

Article Contents

2016, Volume 5, Issue 4: 475-487. Doi: 10.3934/eect.2016015

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Controllability of a basic cochlea model

Scott W. Hansen^1,

1.
Department of Mathematics, Iowa State University, Ames, IA 50011

Received: July 31, 2016

Revised: August 31, 2016

Published: November 2016

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Abstract

Two variations of a basic model for a cochlea are described which consist of a basilar membrane coupled with a linear potential fluid. The basilar membrane is modeled as an array of oscillators which may or may not include longitudinal elasticity. The fluid is assumed to be a linear potential fluid described by Laplace's equation in a domain that surrounds the basilar membrane. The problem of controllability of the system is considered with control active on a portion of the basilar membrane. Approximate controllability is proved for both models and moreover lack of exact controllability is shown to hold when longitudinal stiffness is not included.

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Mathematics Subject Classification: Primary: 93B05, 93C20; Secondary: 74F10, 74K15.

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