A coefficient identification problem for a system of advection-diffusion-reaction equations in water quality modeling

The inverse problem of reconstructing two space-varying coefficients in a system of one-dimensional (1-d) time-dependent advection-diffusion-reaction (ADR) equations is considered. The ADR system can be used as a water quality model which describes the evolution of the biochemical oxygen demand (BOD) and dissolved oxygen (DO) in a river or stream. The coefficients to be reconstructed represents the effect of the deoxygenation and superficial reaeration processes on the DO and BOD concentration in water. Hölder stability estimates for the coefficients of interest are established using the Carleman estimate technique.