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Journal of Applied and Industrial Mathematics

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01-02-2022

Problem of Determining the Two-Dimensional Kernel of the Viscoelasticity Equation with a Weakly Horizontal Inhomogeneity

Authors: D. K. Durdiev, J. Sh. Safarov

Published in: Journal of Applied and Industrial Mathematics | Issue 1/2022

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Abstract

In a domain bounded with respect to the variable \( z \) and having a weakly horizontal inhomogeneity, we consider the problem of determining the convolution kernel \( k(t,x) \), \( t\in [0,T] \), \( x\in {\mathbb R} \), occurring in the viscoelasticity equation. It is assumed that this kernel weakly depends on the variable \( x \) and has a power series expansion in a small parameter \( \varepsilon \). A method is constructed for finding the first two coefficients \( k_{0}(t) \) and \( k_{1 }(t) \) of this expansion. Theorems on the global unique solvability of the problem are obtained.

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Title: Problem of Determining the Two-Dimensional Kernel of the Viscoelasticity Equation with a Weakly Horizontal Inhomogeneity
Authors: D. K. Durdiev
J. Sh. Safarov
Publication date: 01-02-2022
Publisher: Pleiades Publishing
Published in: Journal of Applied and Industrial Mathematics / Issue 1/2022
Print ISSN: 1990-4789
Electronic ISSN: 1990-4797
DOI: https://doi.org/10.1134/S1990478922010033

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