Identification of a point source in a linear advection–dispersion–reaction equation: application to a pollution source problem

Abstract

We consider the problem of identification of a pollution source in a river. The mathematical model is a one-dimensional linear advection-dispersion-reaction equation with the right-hand side spatially supported at a point (the source) and a time-dependent intensity, both unknown. Assuming that the source becomes inactive after the time T * , we prove that it can be identified by recording the evolution of the concentration at two points, one of which is strategic.

Point source estimation via finite element multiple-model Kalman filtering

“…All the results of this section will refer to the system (8) or (8)- (9) in the case (b), under the observability decomposition (10). By exploiting standard results on observability and left invertibility of linear systems, the following theorem can now be stated.…”

“…Both cases of motionless source with unknown position and of moving source are addressed, resorting to the static Multiple Model (MM) and, respectively, dynamic Interacting Multiple Model (IMM) algorithms. It is worth pointing out that the source estimation/identification problem has been also addressed in [10] as an inverse PDE problem, while in the present work it is regarded as a hybrid state estimation problem making use of space discretization.…”

Inverse source problem in an advection–dispersion–reaction system: application to water pollution

“…The above inverse problem (ISP) is different to that considered in our previous study [3], although we are in both cases interested in the identification of source pollution in a river. Indeed, in [3] only the first equation in (1.1) has been considered where the measurements are taken directly on the concentration u.…”

Estimation of river pollution source using the space-time radial basis collocation method

“…Because of strong advection in rivers, pollutants are transported faster and farther due to the dispersion effect, leading to difficulties in detecting the contaminant plume for the recovery of source release information and to computational instability in numerical solutions. Badia et al [5] established identifiability and stability results for identification of pollution point sources. Boano et al [12] applied geostatistical method to estimate a spatially distributed source and independent point sources taking into account the influence of dead zones on transport processes.…”