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Sibirskii Zhurnal Industrial'noi Matematiki, 2013, Volume 16, Number 2, Pages 72–82
(Mi sjim781)
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This article is cited in 33 scientific papers (total in 33 papers)
The problem of determining the one-dimensional kernel of the viscoelasticity equation
D. K. Durdieva, Zh. D. Totievab a Bukhara State University, 11 Mukhammad Iqbol st., 200177 Bukhara, Uzbekistan
b Center of Geophysical Investigations of the Vladikavkaz Scientific Center of the Russian Academy of Sciences and Republic of North Ossetia--Alania, 93a Markov st., 362002 Vladikavkaz, Russia
Abstract:
We consider the integrodifferential system of viscoelasticity equations. The direct problem consists in determining the displacement vector from the initial boundary value problem for this system. Under the assumption that the coefficients of the equation depend only on one space variable $x_3$, the system is reduced to an equation for one component $u_1(x_3,t)$. For this equation, we investigate the problem of finding the kernel belonging to the integral part of the equation. For its determination, an additional condition is given on $u_1(x_3,t)$ for $x_3=0$. The inverse problem is replaced by an equivalent system of integral equations for unknown functions. To this system, we apply the contraction mapping principle. A theorem of global unique solvability is proved and a stability estimate of a solution to the inverse problem is obtained.
Keywords:
inverse problem, stability, delta-function, Lamé coefficients, kernel.
Received: 01.02.2013
Citation:
D. K. Durdiev, Zh. D. Totieva, “The problem of determining the one-dimensional kernel of the viscoelasticity equation”, Sib. Zh. Ind. Mat., 16:2 (2013), 72–82
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https://www.mathnet.ru/eng/sjim781 https://www.mathnet.ru/eng/sjim/v16/i2/p72
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Abstract page: | 820 | Full-text PDF : | 284 | References: | 68 | First page: | 13 |
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