Determining of isotropic medium parameters in a sphere
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 524-530
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We consider an inverse problem for a system of isotropic elasticity equations in a sphere domain. The linearized problem of identification of three characteristics of elastic isotropic medium is investigated. It is supposed that the medium density $\rho(r)$ depends on the radial variable only and the propagation velocity of longitudinal $c(r,\theta,\varphi)$ and transverse $a(r,\theta,\varphi)$ waves can be represented in the form $a^2(r,\theta,\varphi)=a_0^2+a_1(r,\theta,\varphi)$, $c^2(r,\theta,\varphi)=c_0^2+c_1(r,\theta,\varphi)$, where $a_0^2$, $c_0^2$ are some known constants, and unknown functions $a_1(r,\theta,\varphi)$, $c_1(r,\theta,\varphi)$ are small in comparison with the constants $a_0^2$ и $c_0^2$, correspondingly. The uniqueness theorem is proved and estimates of conditional stability of the inverse problem solution are obtained.
Keywords:
inverse problems, isotropic elasticity, conditional stability estimate.
@article{SEMR_2008_5_a46,
author = {T. V. Bugueva},
title = {Determining of isotropic medium parameters in a~sphere},
journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
pages = {524--530},
year = {2008},
volume = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SEMR_2008_5_a46/}
}
T. V. Bugueva. Determining of isotropic medium parameters in a sphere. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 524-530. http://geodesic.mathdoc.fr/item/SEMR_2008_5_a46/