This article is cited in 17 papers

An Inverse Problem for Determining Two Coefficients in an Integrodifferential Wave Equation

D. K. Durdiev

Bukhara State University, Bukhara, Uzbekistan

Abstract: 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, Fourier transform, stability, uniqueness.

UDC: 517.958

Received: 20.11.2008

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