Identification of the pollution source from one-dimensional parabolic equation models

Consider an inverse source problem modeling the pollution source detection in a watershed. The diffusion process due to the point source pollution is governed by a one-dimensional linear parabolic equation with unknown source of the form λ(t)δ(x-s)λ(t)δ(x-s), where s   is the location and λ(t)λ(t) the amplitude of point source. Applying a priori information about the source location and the analytic extension theory, we prove the uniqueness from two interior measurements for the two kinds of boundary state: one is a finite watershed model with zero-Neumann boundary data and the other is an infinite watershed model. Finally, an implementable inversion algorithm together with some numerical examples are presented, which shows the validity of our inversion scheme.