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2 results

Identification of a wave equation generated by a string ∗
Amin Boumenir
Journal: ESAIM: Control, Optimisation and Calculus of Variations / Volume 20 / Issue 4 / October 2014
Published online by Cambridge University Press: 08 August 2014, pp. 1203-1213
Print publication: October 2014
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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.

The transmutation operator for −d2/(w(x) dx2)
Amin Boumenir
Journal: Proceedings of the Royal Society of Edinburgh Section A: Mathematics / Volume 125 / Issue 1 / 1995
Published online by Cambridge University Press: 14 November 2011, pp. 85-98
Print publication: 1995
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We would like to obtain the transmutation operator V, associated with the self-adjoint operators −d2/(w(x) dx2) and (−d2/(w(x) dx2)) + h(x), where w(x) ≎ xa as x → 0. We shall show that V = 1 + K, where K is a lower triangular Volterra operator.