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JOURNALS // Sibirskii Zhurnal Industrial'noi Matematiki // Archive

Sib. Zh. Ind. Mat., 2022 Volume 25, Number 1, Pages 14–38 (Mi sjim1159)

This article is cited in 6 papers

2D kernel identification problem in viscoelasticity equation with a weakly horizontal homogeneity

D. K. Durdieva, J. Sh. Safarovab

a V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, ul. Universitetskaya 4b, Tashkent 100174, Uzbekistan
b Tashkent University of Information Technologies, ul. Amira Temura 108, Tashkent 100084, Uzbekistan

Abstract: We consider the problem of determining the kernel $k(t,x)$, $t\in [0,T]$, $x\in {\Bbb R}$, entering the equation of viscoelasticity in a bounded domain with respect to $z$ with weakly horizontal homogeneity. It is assumed that this kernel weakly depends on the variable $x$ and decomposes into a power series by degrees of the small parameter $\varepsilon$. A method for finding unknown functions $k_{0}$, $k_{1}$ is constructed. The global uniquely solvability and stability theorems are obtained.

Keywords: viscoelasticity equation, inverse problem, delta-function, integral equation, Banach theorem. .

UDC: 517.968.72

Received: 11.08.2021
Revised: 01.10.2021
Accepted: 21.10.2021

DOI: 10.33048/SIBJIM.2022.25.102



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© Steklov Math. Inst. of RAS, 2024