Differential Equations

Global solvability of two unknown variables identification problem in one inverse problem for the integro-differential wave equation

D. K. Durdiev

Dept. of Differential Equations, Bukhara State University, Bukhara, Uzbekistan

Abstract: Identification problem of the two coefficients, one of which is located under the integral sign in a hyperbolic equation and represents memory of the medium is studied, the other one defines a regular part of an impulse source. As an additional information Fourier image of the solution's trace of a direct problem on the hyperplane $y=0$ for two different values of transformation parameters is applied. The global solvability and the estimate of stability of the inverse problem are defined.

Keywords: inverse problem, integro-differential wave equation, hyperbolic equation, agreement condition, uniqueness, stability.

UDC: 517.956.37

MSC: 35L10

Original article submitted 24/XII/2008
revision submitted – 15/II/2009

DOI: 10.14498/vsgtu656

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