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Identification of a wave equation generated by a string

Amin Boumenir (2014)

ESAIM: Control, Optimisation and Calculus of Variations

We show that we can reconstruct two coefficients of a wave equation by a single boundary measurement of the solution. The identification and reconstruction are based on Krein’s inverse spectral theory for the first coefficient and on the Gelfand−Levitan theory for the second. To do so we use spectral estimation to extract the first spectrum and then interpolation to map the second one. The control of the solution is also studied.

Inverse problems on star-type graphs: differential operators of different orders on different edges

Vyacheslav Yurko (2014)

Open Mathematics

We study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.

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