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

A coefficient identification problem (CIP) for a system of one-dimensional advection-reaction equations using boundary data is considered. The advection-reaction equations are used to describe the transportation of pollutants in rivers or streams. Stability for the considered CIP is proved using global Carleman estimates. The CIP is solved using the least-squares approach accompanied with the adjoint equation technique for computing the Fréchet derivatives of the objective functional. Lipschitz-type error estimates of the reconstructed coefficients are proved. Numerical tests are presented to illustrate the performance of the proposed algorithm.