Abstract: The viscoelastic equations with the Lamé coefficients λ and μ, density ρ and viscoelastic coefficients 1 and 1 are considered. All these coefficients are functions of space variable ∈ℝ3 and they are known constants outside ball of radius R centered at the origin. It is supposed that λ, μ and ρ are given smooth functions in ℝ3 , while 1 and 1 are unknown in . The problem of recovering the latter functions from a given information about solutions of some the Cauchy problems for viscoelastic equations is studied. At first, running plain waves going in the homogeneous media from infinity in direction ∈ 2 are considered. These waves are pure compressive or shear ones of the delta-image form. They are passed thorough ball and their amplitudes are measured on the boundary of for all ∈ 2 . It is shown that this information allows to reduce the origin problem to two problems of the inversion of the ray transforms for a family of geodesic lines related to two Riemannian metrics. The latter problems are well studied, particularly, stability and uniqueness theorems are known for theirs. The reducing of the original problem of recovering desired coefficients to linear inversion problems opens a good way for its numerical solution.

Cite: Romanov V.G.
Recovering Lamé kernels in viscoelastic equations and ray transforms
Journal of Inverse and Ill-Posed Problems. 2026. DOI: 10.1515/jiip-2025-0101 WOS Scopus OpenAlex

Dates:

Submitted:	Dec 14, 2025
Accepted:	Jan 24, 2026
Published online:	Feb 20, 2026

Identifiers:

≡ Web of science:	WOS:001694686700001
≡ Scopus:	2-s2.0-105030569087
≡ OpenAlex:	W7130607070

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