Оценка условной устойчивости решения обратной задачи для уравнения акустики

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.