Modeling the Process of Critical Exhaustion of Oxygen in a River Caused by Exponential Source of Pollution

The analysis and improvement of the river's change dynamics are critical to the global investigation of water quality issues. This study investigates the mathematical model representation of one dimension of a pair of advection-dispersion equations. These equations pertain to the concentrations of both pollutants and dissolved oxygen. Certain terms, which demonstrate an increase in the decay rate of pollution through exponential sources and assume a decreasing river's cross-sectional measurement, lead to the diminished oxygen levels observed in this study. The crucial points are demonstrated using both analytical and numerical analysis of the steady-state model, which allows for examining multiple situations about the elimination of oxygen and aquatic survival in a river with severe pollution.