On some inverse problems for a nonlinear transport equation

Inverse problems for nonlinear transport or the one-way wave equation in one spatial dimension are considered. Analytic solutions to the inverse problems are given and it is shown, for some signalling problems, that the inverse problem of determination of a wave speed functional is well-posed, and that the wave speed can be uniquely determined. However, it is shown that the inverse problems of reconstruction of a source functional are ill-posed, although the source is still uniquely determined.