On optimal solution of an inverse air pollution problem: Theory and numerical approach

A three-dimensional dispersion air pollution model with point sources is considered in a limited region. The adjoint model and the duality principle are used to pose a variational short-term control problem with the aim of determining optimal emission rates of the sources. The existence and uniqueness of the optimal control problem solution are proved. A numerical scheme using a process of orthogonal projections is given for approximating the optimal solution. The computing efficiency of the scheme is shown. Numerical results obtained in the case of a single point source demonstrate the method’s ability.