Inverse source problem in a 2D linear evolution transport equation: detection of pollution source

Abstract

This article deals with the identification of a time-dependent source spatially supported at an interior point of a 2D bounded domain. This source occurs in the right-hand side of an evolution linear advection-dispersion-reaction equation. We address the problem of localizing the source position and recovering the history of its time-dependent intensity function. We prove the identifiability of the sought source from recording the state on the outflow boundary of the controlled domain. Then, assuming the source intensity function vanishes before reaching the final control time, we establish a quasi-explicit identification method based on some exact boundary controllability results that enable to determine the elements defining the sought source using the records of the state on the outflow boundary and of its flux on the inflow boundary. Some numerical experiments on a variant of the surface water biological oxygen demand pollution model are presented.

Keywords:

• inverse source problem
• exact boundary controllability
• optimization
• advection-dispersion-reaction equation
• surface water pollution