Abstract: —A system of acoustic equations in which the Lam´e parameter has a memory (i.e., depends on the history) is considered. The dependence has a specific form and is described by an integral convolution operator whose kernel is the product of two functions, one depending on the space coordinates and the other, on time. For this system of equations, we study an acoustic tomography problem in which three functions, namely, the speed of acoustic waves, the medium density, and the component of the memory kernel depending on the space variables, should be reconstructed. To solve this problem, we use information on a series of solutions of direct problems for the acoustic equations with point sources. This information is given for a finite time interval at the points of some sphere inside which the coefficients to be recovered are assumed to be unknown. We show that the problem in question can be reduced to the inverse kinematic problem for reconstructing the speed of sound and two X-ray tomography problems to be solved consecutively.

Cite: Romanov V.G.
Acoustic Tomography Problem with Memory
Differential Equations. 2026. V.62. N2. P.273-281. DOI: 10.1134/s0012266126020059 WOS Scopus РИНЦ OpenAlex

Original: Романов В.Г.
Задача акустической томографии с памятью
Дифференциальные уравнения. 2026. Т.62. №2. С.175-185. DOI: 10.7868/S3034503026020038 РИНЦ

Dates:

Submitted:	Jan 12, 2026
Accepted:	Jan 22, 2026
Published print:	Aug 20, 2026
Published online:	Aug 20, 2026

Identifiers:

≡ Web of science:	WOS:001854309400009
≡ Scopus:	2-s2.0-105048108787
≡ Elibrary:	91954692
≡ OpenAlex:	W7203834512

Altmetrics: