Geodesic
An Identification Problem of Memory Function of a~Medium and the Form of an Impulse Source
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 2, pp. 127-136

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In the paper the problem of identification of two functions, one of which is under the integral sign in a hyperbolic equation and represents the medium's memory, the other one defines the regular part of an impulse source is considered. As additional information Fourier image trace solution of a direct problem on the hyperplane $y=0$ for two different values of transformation parameters is given. The estimate of stability of the solution of the inverse problem and the uniqueness theorems is proved.
Keywords: inverse problem, hyperbolic equation, stability, uniqueness. 
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Durdimurod K. Durdiev. An Identification Problem of Memory Function of a~Medium and the Form of an Impulse Source. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 2, pp. 127-136. http://geodesic.mathdoc.fr/item/JSFU_2009_2_2_a0/