Zh. D. Totieva, “Two-dimensional inverse problem for a viscoelasticity equation in a vertically inhomogeneous medium”, Sib. Zh. Ind. Mat., 2025, Volume 28, Number 1,Pages <nobr>80

Two-dimensional inverse problem for a viscoelasticity equation in a vertically inhomogeneous medium

Zh. D. Totieva^ab

^a Southern Mathematical Institute, Vladikavkaz Scientific Center, Russian Academy of Sciences, Vladikavkaz, 362027 Russia
^b North Caucasus Center for Mathematical Research of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, selo Mikhailovskoe, North Ossetia–Alania, 363110 Russia

Abstract: The two-dimensional inverse problem of determining the kernel of an elasticity equation of memory type is studied. It is assumed that the coefficients of the equations depend on only one spatial variable. Applying the linearization principle, the inverse problem is reduced to an equivalent linear system of integral equations. The generalized principle of compressed maps is applied to the latter in the space of continuous functions. The theorem of unique solvability is proved and an estimate of the stability of the solution to the inverse problem is obtained.

Keywords: inverse problem, integro-differential equation, viscoelasticity, stability, delta function, kernel.

UDC: 517.958

Received: 11.08.2023
Revised: 31.10.2024
Accepted: 26.03.2025

DOI: 10.33048/SIBJIM.2025.28.106