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

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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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Authors and Affiliations

  1. Romanovskii Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, 100170, Uzbekistan

    D. K. Durdiev & J. Sh. Safarov

  2. Tashkent University of Information Technologies, Tashkent, 100084, Uzbekistan

    J. Sh. Safarov

Authors
  1. D. K. Durdiev
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  2. J. Sh. Safarov
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Correspondence to D. K. Durdiev or J. Sh. Safarov.

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Translated by V. Potapchouck

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Durdiev, D.K., Safarov, J.S. Problem of Determining the Two-Dimensional Kernel of the Viscoelasticity Equation with a Weakly Horizontal Inhomogeneity. J. Appl. Ind. Math. 16, 22–44 (2022). https://doi.org/10.1134/S1990478922010033

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  • DOI: https://doi.org/10.1134/S1990478922010033

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