Inverse eigenvalue problem for a vibration of a string with viscous drag. (English) Zbl 0717.73046

A pair of eigenvalue problems is considered describing eigenvibrations of a string with viscous drag: \[ d/dx[T(x)(dv(x)/dx)]-\lambda k(x)v(x)=\lambda^ 2\rho (x)v(x)\quad (0\leq x\leq 1), \] and \[ v(0)=v(1)=0\quad or\quad v(0)=dv/dx(1)=0. \] It is shown that all the eigenvalues of these two problems uniquely determine both a tension T and a linear mass density \(\rho\), provided that the coefficient of viscous drag k(x) is a given nonzero constant function.
Reviewer: E.Syrkin


74H45 Vibrations in dynamical problems in solid mechanics
74B99 Elastic materials
74H99 Dynamical problems in solid mechanics
34A55 Inverse problems involving ordinary differential equations
74J25 Inverse problems for waves in solid mechanics
74K05 Strings
34L05 General spectral theory of ordinary differential operators
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