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Dal'nevostochnyi Matematicheskii Zhurnal, 2013, Volume 13, Number 2, Pages 209–221 (Mi dvmg264)  

This article is cited in 9 scientific papers (total in 9 papers)

A problem of determining the kernel of integrodifferential wave equation with weak horizontal properties

D. K. Durdiev, Z. R. Bozorov

Bukhara State University
Full-text PDF (141 kB) Citations (9)
References:
Abstract: An inverse problem of determining the two-dimensional kernel of integro-differential wave equation in medium of weak horizontal properties is considered. Herein the initial data are equal to zero. The boundary condition of Neyman type is given at the boundary of semi-plane is an impulse function. As an additional information the semi-plane line mode is given. It is assumed that the unknown kernel has the form of $K(t)=K_0(t)+\varepsilon x K_1(t)+\dots$, where $\varepsilon$ is a small parameter. In the work, the method of finding $K_0$, $K_1$ with precision correction, having the order $O(\varepsilon^2)$ is developed. For this, by Fourier transformation the problem is brought to the sequence of two one-dimensional inverse problems of determining $K_0$, $K_1$. The first inverse problem for $K_0$ is reduced to the system of nonlinear integral equations of Volterra type relative to the unknown functions, and the second being brought to the system of linear integral equations. Theorems that characterize the unique solvability of determining unknown functions for any fixed intercept are proved.
Key words: wave equation, inverse problem, delta function, Fourier transformation, integral equation.
Received: 09.04.2013
Document Type: Article
UDC: 517.958
MSC: 35L10
Language: Russian
Citation: D. K. Durdiev, Z. R. Bozorov, “A problem of determining the kernel of integrodifferential wave equation with weak horizontal properties”, Dal'nevost. Mat. Zh., 13:2 (2013), 209–221
Citation in format AMSBIB
\Bibitem{DurBoz13}
\by D.~K.~Durdiev, Z.~R.~Bozorov
\paper A problem of determining
the kernel of integrodifferential wave equation with weak
horizontal properties
\jour Dal'nevost. Mat. Zh.
\yr 2013
\vol 13
\issue 2
\pages 209--221
\mathnet{http://mi.mathnet.ru/dvmg264}
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  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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