ON INVERSE SOURCE PROBLEMS FOR THE ONE-WAY WAVE-EQUATION

Inverse problems are considered for the linear one-way wave equation o r transport equation. The equation is one-dimensional and nonstationar y, that is, it has spatial and time-dependent wave speed and dissipati on. In particular a number of inverse source reconstruction problems a re considered. Both theoretical and numerical results are given for th e methods examined. In particular it is shown that the source reconstr uction is unique, when the source function is separable as a function of time and space, for the inverse problems discussed. It is shown tha t the inverse source problems are ill-posed and regularisation is intr oduced to provide well-posed problems.