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Determining the Kernel of the Viscoelasticity Equation in a Medium with Slightly Horizontal Homogeneity

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Abstract

Under study is the inverse problem of determining the two-dimensional kernel for a system of viscoelasticity equations in a medium with slightly horizontal homogeneity in a half-space. The direct initial-boundary value problem for the displacement function contains zero initial data and the Neumann condition of a special form. The field of displacements of medium points is given for x3 − 0 as additional information. We assume that the kernel decomposes into an asymptotic series, construct some method for determining the kernel with accuracy of O(ε2) where ε is a small parameter, and prove the theorems of global unique solvability and stability of the solution to the inverse problem.

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  1. Southern Mathematical Institute, North-Ossetian State University, Vladikavkaz, Russia

    Zh. D. Totieva

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  1. Zh. D. Totieva
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Correspondence to Zh. D. Totieva.

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Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 2, pp. 453–475.

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Totieva, Z.D. Determining the Kernel of the Viscoelasticity Equation in a Medium with Slightly Horizontal Homogeneity. Sib Math J 61, 359–378 (2020). https://doi.org/10.1134/S0037446620020172

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  • DOI: https://doi.org/10.1134/S0037446620020172

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