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Mat. Zametki, 2018, Volume 103, Issue 1, Pages 129–146 (Mi mz10752)  

This article is cited in 2 scientific papers (total in 2 papers)

The Problem of Finding the One-Dimensional Kernel of the Thermoviscoelasticity Equation

Zh. D. Totievaab, D. K. Durdievc

a Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz
b North Ossetian State University after Kosta Levanovich Khetagurov, Vladikavkaz
c Bukhara State University

Abstract: The problem of determining the kernel $h(t)$, $t\in[0,T]$, appearing in the system of integro-differential thermoviscoelasticity equations is considered. It is assumed that the coefficients of the equations depend only on one space variable. The inverse problem is replaced by the equivalent system of integral equations for unknown functions. The contraction mapping principle with weighted norms is applied to this system in the space of continuous functions. A global unique solvability theorem is proved and an estimate of the stability of the solution of the inverse problem is obtained.

Keywords: inverse problem, stability, delta function, Lamé coefficients, kernel.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm10752

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English version:
Mathematical Notes, 2018, 103:1, 118–132

Bibliographic databases:

UDC: 517.958
Received: 24.04.2015
Revised: 20.12.2016

Citation: Zh. D. Totieva, D. K. Durdiev, “The Problem of Finding the One-Dimensional Kernel of the Thermoviscoelasticity Equation”, Mat. Zametki, 103:1 (2018), 129–146; Math. Notes, 103:1 (2018), 118–132

Citation in format AMSBIB
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\by Zh.~D.~Totieva, D.~K.~Durdiev
\paper The Problem of Finding the One-Dimensional Kernel of the Thermoviscoelasticity Equation
\jour Mat. Zametki
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\vol 103
\issue 1
\pages 129--146
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\crossref{https://doi.org/10.4213/mzm10752}
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\transl
\jour Math. Notes
\yr 2018
\vol 103
\issue 1
\pages 118--132
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  • https://doi.org/10.4213/mzm10752
  • http://mi.mathnet.ru/eng/mz/v103/i1/p129

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. K. Durdiev, Zh. D. Totieva, “The problem of determining the one-dimensional matrix kernel of the system of viscoelasticity equations”, Math. Methods Appl. Sci., 41:17 (2018), 8019–8032  crossref  mathscinet  zmath  isi
    2. Zh. D. Totieva, “K voprosu issledovaniya zadachi opredeleniya matrichnogo yadra sistemy uravnenii anizotropnoi vyazkouprugosti”, Vladikavk. matem. zhurn., 21:2 (2019), 58–66  mathnet  crossref
  • Математические заметки Mathematical Notes
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