Existence and uniqueness of an inverse problem for a hyperbolic system of lidar probing (cloud properties)

Over the years, lidar probing has been widely used to identify cloud properties (e.g. thickness and concentration) in an atmosphere. The authors examine the inverse problem of reconstructing the cloud concentration from the lidar signal. The problem that is considered is a hyperbolic system of first-order partial differential equations in a semi-infinite medium. The issues of existence, uniqueness and continuous dependence on initial data of the inverse problem are addressed.