A Mathematical Model of Oxygen Dependency on Temperature and Pollutant Concentration in a River

Abstract

We formulate a model of a set of advection diffusion partial differential equations governing the concentration of pollutant and oxygen in a river. It is assumed that the concentration of dissolved oxygen is strongly influenced by temperature gradient and the concentration of pollutant is primarily influenced by factors other than temperature, such as the rate of pollutant input into the river. We use asymptotic behavior of the solutions to show that when a river is highly polluted, a slight change in temperature leads to a hypoxia.