Identification of point sources in two-dimensional advection-diffusion-reaction equation: application to pollution sources in a river. Stationary case

We consider the problem of determining pollution sources in a river by using boundary measurements. The mathematical model is a two-dimensional advection-diffusion-reaction equation in the stationary case. Identifiability and a local Lipschitz stability results are established. A cost function transforming our inverse problem into an optimization one is proposed. This cost function represents the difference between the two solutions computed from the prescribed and measured data respectively. This representation is achieved by using values of these two solutions inside the domain. Numerical results are performed for a rectangular domain. These results are compared to those obtained by using a classical least squares regularized method.