An optimal control model for the surface runoff contamination of a large river basin (Q2745325)

The aim of this paper is to develop an optimal control model that explicitly incorporates the inter-subbasin variations in pollutant loads, benefits, and environmental damage costs into a basin-wide management framework. Temporal and spatial dynamics of pollutant are simulated by the modified advection-diffusion partial differential equation. The linear flow of pollutant concentration along the course of a river is assummed to be governed by a classical advection-diffusion process (J. L. Schoor, 1985). At pre-determined irregular intervals along a river continuum, point sources of pollutant (each representing a subbasin) are assumed to exist and to contribute to the pollutant flow. The Dirac delta function is used by the authors to represent the longitudinal location of each pollutant influx node on the river continuum. The possibility of natural assimilation of the poolutant is also accounted for the model by adding a recharge rate term to the equation.NEWLINENEWLINENEWLINEThe paper is organized as follows: Section 2 introduces the conditiom of optimal pollution control and discusses its economic interpretation and management implications. Section 3 states the assumptions, defines the solution space, and proves the existence of an optimal control. Section 4 derives a characterization of the optimal control in terms of an optimality system, viz. the state problem coupled with its adjoint problem. The uniqueness of the solutions for the optimality system is obtained, provided that the time internal is sufficiently small. This entails the uniqueness for the considered optimal control.