Geodesic
A conditional stability estimate for solution of an inverse problem for the acoustic equation
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 142-164

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We consider the multidimensional inverse problem for the acoustic equation $u_{tt}=c^{2}\Bigl(\Delta u-\nabla\ln\rho\cdot\nabla u\Bigr)$ in a medium filling interior of a cylinder infinite with respect to the variable $z$. We assume that the velocity function $c(r)$ is known. The problem of unique determination of the density function $\rho (r, \varphi, z)$ is considered in the linear approximation. The conditional stability estimation is obtained.
Keywords: inverse problems, acoustic equation, conditional stability estimate. 
@article{SEMR_2014_11_a60,
     author = {T. V. Bugueva},
     title = {A conditional stability estimate for solution of an inverse problem for the acoustic equation},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {142--164},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a60/}
}
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T. V. Bugueva. A conditional stability estimate for solution of an inverse problem for the acoustic equation. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 142-164. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a60/