We study optimal control of systems of distributed parameters applied to problems of ambient pollution. The model consists of a parabolic partial differential equation 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 us to calculate the pollution concentration that is poured in a region of the space in such a way that at time t = T, the pollution concentration is as close as possible to the acceptable maximum concentration in the environment. We characterise the optimal control to obtain an optimality system that allows the numerical calculation of the problem and show the convergence of the method. As application, we study the case of the contamination of a river with mercury (Hg) in water without movement and with movement. We present some numerical experiments.