Geodesic
An Inverse Problem for Determining Two Coefficients in an~Integrodifferential Wave Equation
Sibirskij žurnal industrialʹnoj matematiki, Tome 12 (2009) no. 3, pp. 28-40

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For the equation of wave propagation in the half-space filled with some medium, we consider the problem of determining the wave propagation velocity which depends only on the variable $y$ and the memory functions of the medium. There is a point-like pulse source on the boundary of the half-space. We show that both unknown functions of one variable are uniquely determined by the Fourier image with respect to $x$ of the solution to the direct problem on the boundary of the half-space. We estimate the stability of the solution to the problem.
Keywords: inverse problem, stability, uniqueness.
Mots-clés : Fourier transform 
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     author = {D. K. Durdiev},
     title = {An {Inverse} {Problem} for {Determining} {Two} {Coefficients} in {an~Integrodifferential} {Wave} {Equation}},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {28--40},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2009_12_3_a3/}
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D. K. Durdiev. An Inverse Problem for Determining Two Coefficients in an~Integrodifferential Wave Equation. Sibirskij žurnal industrialʹnoj matematiki, Tome 12 (2009) no. 3, pp. 28-40. http://geodesic.mathdoc.fr/item/SJIM_2009_12_3_a3/