In this work we optimize different issues related to phytoremediation techniques for heavy metals removal from shallow water, by means of a combination of mathematical modeling, optimal control of partial differential equations and numerical optimization. We introduce, analyze and solve a 2D mathematical system of nonlinear partial differential equations representing the concentrations of heavy metals, algae and nutrients in large waterbodies. Then, we formulate an optimal control problem related to the optimization of the phytoremediation process. In particular, we determine the minimal quantity of algae to be used in the heavy metals remediation process, and locate the optimal place for such algal mass. We also propose two different full algorithms for computing the numerical solution of the control problem and, finally, we present several numerical results for a realistic case.Ministerio de Economía y Competitividad | Ref. MTM2015-65570-
