Reconstruction of a passive tracer boundary source in an open water area

Marine pollution is one of the most serious environmental problems nowadays. Identification of sources of contaminants is among the main objectives of environmental researchers. In such problems pollutants are sometimes considered as passive tracers. In this paper, a problem of detecting and localization of the passive tracer boundary sources in an open water area is considered. A mathematical model of the sea surface pollution spread based on the system of linear unsteady convection-diffusion-reaction equations is used. The inverse problem of restoring the pollution sources on the domain boundary is formulated under the consideration that the pollution concentration data are given. The method based on the theory of adjoint equations and optimal control is used. The iterative algorithm for the solution of the problem is proposed. The article presents the results of the numerical experiment on application of the proposed algorithm to the problem of recovering pollution sources on the Black Sea coastline.