LeVeque, Randall J.; Peskin, Charles S.; Lax, Peter D. Solution of a two-dimensional cochlea model using transform techniques. (English) Zbl 0576.76130 SIAM J. Appl. Math. 45, 450-464 (1985). Summary: We study the propagation of waves on the basilar membrane, a thin elastic plate immersed in the fluid-filled inner ear, using a two-dimensional linear model. Since the basilar membrane has an exponentially increasing compliance, Fourier transforming these equations gives rise to an unusual boundary value problem for an analytic function in the complex plane. We describe a general technique for solving such equations and apply it to the cochlea model. The resulting expression for the Fourier transform can be used to deduce important features of the cochlea wave. This approach also serves as the basis for an efficient numerical method to approximate the cochlea wave using fast Fourier transforms. Cited in 5 Documents MSC: 76Z05 Physiological flows 92C10 Biomechanics 92C40 Biochemistry, molecular biology Keywords:functional equation; waves on the basilar membrane; thin; two-dimensional linear model; Fourier transform; boundary value problem; analytic function; cochlea model PDFBibTeX XMLCite \textit{R. J. LeVeque} et al., SIAM J. Appl. Math. 45, 450--464 (1985; Zbl 0576.76130) Full Text: DOI