Optimal control of advection-diffusion problems for cropping systems in polluted soils

Abstract The article studies the nutrient transfer mechanism for cropping systems in polluted soils from a mathematical and optimal control point of view. The problem under consideration is governed by an advection-diffusion PDE in a bounded domain. The existence of a solution is obtained. We also determine the optimal amount of required nutrients at the root surface for plants where the soil is polluted by an unknown source. The characterization of the optimal control by a singular optimality system is obtained.