Title: M. M. Lavrentiev-type systems and reconstructing parameters of viscoelastic media.
Authors: Kokurin, Mikhail Yu.
Abstract: We consider a nonlinear coefficient inverse problem of reconstructing the density and the memory matrix of a viscoelastic medium by probing the medium with a family of wave fields excited by moment tensor point sources. A spatially non-overdetermined formulation is investigated, in which the manifolds of point sources and detectors do not coincide and have a total dimension equal to three. The requirements for these manifolds are established to ensure the unique solvability of the studied inverse problem. The results are achieved by reducing the problem to a chain of connected systems of linear integral equations of the M. M. Lavrentiev type.
Subjects: INVERSE problems; BIHARMONIC equations; INTEGRAL equations; DENSITY matrices; LINEAR equations
Publication: Journal of Inverse & Ill-Posed Problems, 2024, Vol 32, Issue 5, p1015
ISSN: 0928-0219
Publication type: Academic Journal
DOI: 10.1515/jiip-2024-0009

M. M. Lavrentiev-type systems and reconstructing parameters of viscoelastic media.

Kokurin, Mikhail Yu.