Approximate boundary controllability of wave equation with mixed boundary conditions and sound-speed reconstruction

We consider acoustical tomography problem: to find a variable speed of sound in a bounded domain Ω by partial boundary measurements using the Boundary Control method. We use Neumann controls which are located at Σ × [0, T], where Σ is an open set of the boundary ∂Ω, T is a sufficiently large observation time. Boundary measurements are given at Σ × [0, 2T ]. The pressure at another part of the boundary is assumed to be zero.