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Sibirsk. Mat. Zh., 2017, Volume 58, Number 3, Pages 553–572 (Mi smj2880)  

This article is cited in 3 scientific papers (total in 3 papers)

The problem of determining the one-dimensional kernel of the electroviscoelasticity equation

D. K. Durdieva, Zh. D. Totievabc

a Bukhara State University, Bukhara, Uzbekistan
b Geophysics Institute, Vladikavkaz, Russia
c North-Ossetian State University, Vladikavkaz, Russia

Abstract: We consider the problem of finding the kernel $K(t)$, for $t\in[0,T]$, in the integrodifferential system of electroviscoelasticity. We assume that the coefficients depend only on one spatial variable. Replacing the inverse problem with an equivalent system of integral equations, we apply the contraction mapping principle in the space of continuous functions with weighted norms. We prove a global unique solvability theorem and obtain a stability estimate for the solution to the inverse problem.

Keywords: inverse problem, stability, delta-function, elasticity moduli, kernel.

DOI: https://doi.org/10.17377/smzh.2017.58.307

Full text: PDF file (337 kB)
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English version:
Siberian Mathematical Journal, 2017, 58:3, 427–444

Bibliographic databases:

UDC: 517.958
MSC: 35R30
Received: 06.05.2016
Revised: 24.10.2016

Citation: D. K. Durdiev, Zh. D. Totieva, “The problem of determining the one-dimensional kernel of the electroviscoelasticity equation”, Sibirsk. Mat. Zh., 58:3 (2017), 553–572; Siberian Math. J., 58:3 (2017), 427–444

Citation in format AMSBIB
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\paper The problem of determining the one-dimensional kernel of the electroviscoelasticity equation
\jour Sibirsk. Mat. Zh.
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\pages 553--572
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\crossref{https://doi.org/10.17377/smzh.2017.58.307}
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\issue 3
\pages 427--444
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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. Meth. Appl. Sci., 41:17 (2018), 8019–8032  crossref  mathscinet  zmath  isi
    2. Zh. D. Totieva, “The problem of determining the piezoelectric module of electroviscoelasticity equation”, Math. Meth. Appl. Sci., 41:16 (2018), 6409–6421  crossref  mathscinet  zmath  isi  scopus
    3. Zh. D. Totieva, “K voprosu issledovaniya zadachi opredeleniya matrichnogo yadra sistemy uravnenii anizotropnoi vyazkouprugosti”, Vladikavk. matem. zhurn., 21:2 (2019), 58–66  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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