Theory of Optimal Control Applied to Problems of Ambiental Pollution

We study the theory of optimal control of systems of distributed parameters and apply to problems of ambient pollution. The model consists of a partial differential equation of parabolic type that models the transport of a pollutant in an incompressible viscous fluid, with boundary conditions and initial value; that is, in our model we consider the velocity that the pollutant propagates in the environment. The developed mathematical modelling allows to calculate the pollution concentration that is spread out in a determined region Ω of space, in such a way that at the time t = T , the pollution concentration is the closest as possible to the acceptable maximum concentration in the environment. We show the existence and uniqueness of the state system and a unique optimal control on a set of permissible functions. We characterize the optimal control to obtain an optimality system that allows the numerical calculation of the problem and show the convergence of the method. As an application, we study the case of the contamination of a river/lagoon by mercury (Hg) in water in movement and still water. The primary aim of this work is to minimize, through the controls, the effect caused by the debris of the pollutant agent. We present some numerical experiments. ——————————————————