This monograph is dedicated to the development of a special method for the investigation of systems with incomplete data. The systems are modelled with evolution partial differential systems for which initial and boundary conditions are given. The problem is as follows: if, for instance, the source entry in the system and the initial conditions are only partially known, find a way to get information about the source entry, independent of noise around the initial conditions, or a way to get information about the initial conditions that are assumed independent of noise in the source entry. The necessity to consider these kinds of problems has its roots in solving practical problems, for instance, in oceanography, meteorology or estimation of pollution, where indeed measurements contain errors or cannot be carried out completely.