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On the determination of the coefficients in the viscoelasticity equations

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Abstract

For the integrodifferential viscoelasticity equations, we study the problem of determining the coefficients of the equations and the kernels occurring in the integral terms of the system of equations. The density of the medium is assumed to be given. We suppose that the inhomogeneity support of the sought functions is included in some compact domain B 0. We consider a series of inverse problems in which an impulse source is concentrated at the points y of the boundary of B 0. The point y is the parameter of the problem. The given information about the solution is the trace of the solution to the Cauchy problem with zero initial data. This trace is given on the boundary of B 0 for all y ∈ ∂B 0 and for a finite time interval. The main result of the article consists in obtaining uniqueness theorems for a solution to the initial inverse problem.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    V. G. Romanov

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  1. V. G. Romanov
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Correspondence to V. G. Romanov.

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Original Russian Text Copyright © 2014 Romanov V.G.

The author was supported by the Russian Foundation for Basic Research (Grant 14-01-00208-a), the Siberian Division of the Russian Academy of Sciences (Integration Project No. 14), the Interdisciplinary Project for 2013 (Grant No. 12) of the National Academy of Sciences of Ukraine and the Siberian Division of the Russian Academy of Sciences, and the Department of Education and Science of Kazakhstan (Grant 1843-2012).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 3, pp. 617–626, May–June, 2014.

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Romanov, V.G. On the determination of the coefficients in the viscoelasticity equations. Sib Math J 55, 503–510 (2014). https://doi.org/10.1134/S0037446614030124

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  • DOI: https://doi.org/10.1134/S0037446614030124

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