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This article is cited in 4 scientific papers (total in 4 papers)
MATHEMATICS
The problem of determining the memory of an environment with weak horizontal heterogeneity
D. K. Durdievab, J. Sh. Safarovcb a Bukhara State University, 11, Muhammad Igbol st., Bukhara, 200118, Uzbekistan
b Institute of Mathematics named after V. I. Romanovsky,
the AS of the Republic of Uzbekistan, 46, ul. Universitetskaya, Tashkent, 100174, Uzbekistan
c Tashkent University of Information Technologies
named after Muhammad al-Khwarizmi, 108, Amir Timur Ave., Tashkent, Uzbekistan, 100200
Abstract:
The problem of determining the convolutional kernel $k(t,x)$, $t>0$, $x \in {\mathbb{R}}$, included in a hyperbolic integro-differential equation of the second order, is investigated in a domain bounded by a variable $z$ and having weakly horizontal heterogeneity. It is assumed that this kernel weakly depends on the variable $x$ and decomposes into a power series by degrees of a small parameter $\varepsilon$. A method for finding the first two coefficients $k_{0}(t)$, $k_{1}(t)$ of this expansion is constructed according to the given first two moments in the variable $x$ of the solution of the direct problem at $z=0$.
Keywords:
integro-differential equation, inverse problem, the Dirac delta function, the kernel of the integral, the norm.
Received: 13.04.2022 Accepted: 03.08.2022
Citation:
D. K. Durdiev, J. Sh. Safarov, “The problem of determining the memory of an environment with weak horizontal heterogeneity”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 32:3 (2022), 383–402
Linking options:
https://www.mathnet.ru/eng/vuu816 https://www.mathnet.ru/eng/vuu/v32/i3/p383
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Abstract page: | 173 | Full-text PDF : | 63 | References: | 17 |
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