Degree Type

Dissertation

Date of Award

2006

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Scott Hansen

Abstract

The standard 2-dimensional cochlear model consists of a 1-dimensional elastic structure, modeling the basilar membrane, surrounded by an incompressible 2-dimensional fluid within a 2-dimensional cochlear cavity. The dynamics are typically driven by a pressure differential across the basilar membrane transmitted through the round and oval windows (a portion of the boundary of the cochlear). First we describe a model in which the basilar membrane is modeled as an infinite array of oscillators and the fluid is described by Laplace's equation. In this setting, we show that the coupled system is approximately controllable with control acting on an arbitrary open set of the basilar membrane. Second we consider a cochlear model where the basilar membrane has a longitudinal elastic tension. In this case the differential equations describing the dynamics of the system have variable coefficients. We first change the variables and then use the method of multipliers to prove exact controllability result.

DOI

https://doi.org/10.31274/rtd-180813-217

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Isaac Chepkwony

Language

en

Proquest ID

AAI3243569

File Format

application/pdf

File Size

76 pages

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