Inverse problem solution for vibration equation with directed sources (Q1281211)

The equation \[ \frac{\partial^2 w}{\partial t^2} - \frac{\partial^2 w}{\partial x^2} - q(x)w= 0, \quad x>0,\;t >0 \] with initial-boundary conditions is considered. The coefficient \(q(x)\) is to be reconstructed from corresponding information concerning \(w(x,t)\). There is derived a reconstruction algorithm, and uniqueness theorems are proved using the theory of generalized functions and Laplace transformation.