Location and density determination for a source with impulse derivative time variation

In this study an inverse source problem related to the source density f₀(x) which is a function of bounded support and taking place in the wave equation Δu(x, t) - (1/c²) ∂² u(x, t) / ∂t² = - f₀ (x)δ´(t) is considered. An explicit expression of the solution is given in terms of the surface integral of the data which is measured on the boundary S of a convex domain D during certain finite time interval [0, T]. An illustrative example shows the applicability as well as the effectiveness of the method.