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Methods of boundary control theory in the nonstationary inverse problem for an inhomogeneous string

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Abstract

An approach to inverse problems based on the boundary control theory is developed. The dynamic problem to recover a density of an inhomogeneous string via its free endopoint oscillations generated by an instantaneous force source is proposed. The problem is to determine the coefficient ρ(x)>0 in the equation ρ(x)utt(x, t)−uxx(x, t)=0(x, t>0) with the conditions u|<0=0, ux(0, t)=δ(t) by using a known function (response) u(0, t)=r(t) (t>0). The authors propose an algorithm based upon the approach and demonstrate its numerical efficiency in the test problems including those for nonmonotone ρ(x)'s. Bibliography: 12 titles.

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Literature Cited

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Authors
  1. M. I. Belishev
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  2. T. L. Sheronova
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Additional information

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 186, pp. 37–49, 1990.

Translated by T. N. Surkova.

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Belishev, M.I., Sheronova, T.L. Methods of boundary control theory in the nonstationary inverse problem for an inhomogeneous string. J Math Sci 73, 320–329 (1995). https://doi.org/10.1007/BF02362816

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  • DOI: https://doi.org/10.1007/BF02362816

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