dc.contributor.author Cox, Steven J.Embree, Mark 2018-06-19T17:46:06Z 2018-06-19T17:46:06Z 2010-08 Cox, Steven J. and Embree, Mark. "Reconstructing an Even Damping from a Single Spectrum." (2010) https://hdl.handle.net/1911/102166. https://hdl.handle.net/1911/102166 We consider the wave equation on a finite interval with fixed ends and nonuniform viscous damping. We prove that the spectrum of the associated damped wave operator uniquely determines an even damping. We then develop a refined asymptotic formula for the high frequencies. When the damping is even about the domain's midpoint, terms in this expansion are Fourier coefficients for functions of the damping. Furthermore, the expansion is often quite accurate even at low frequencies, thus suggesting a simple numerical procedure for reconstructing even damping coefficients from measured eigenvalues. Computational examples illustrate the efficacy of this procedure, even in the presence of noise. 18 pp Reconstructing an Even Damping from a Single Spectrum Technical report August 2010 TR10-25 Text
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