Mathematical Modelling

Direct and inverse problem of organic pollution propagation

S. P. Semenov, A. A. Finogenov

Yugra State University, Khanty-Mansiysk, Russian Federation

Abstract: This paper provides a refined mathematical model of the river pollution consisting of two nonlinear ordinary differential equations for pollutant and dissolved oxygen concentra- tions and studies of the impact of the biochemical coefficient in the Michaelis-Menten formula on the rate of dissolved oxygen recovery and pollutant decomposition. A stationary solution is found and a phase portrait of the dynamic system is constructed numerically. A numerical assessment of the dynamics of pollutant distribution in river waters along its length is carried out. An inverse problem is stated and a numerical method for its solving is proposed. The proposed mathematical model and the method for solving the inverse problem allow to effectively study the distribution of organic pollutants and predict their impact on aquatic ecosystems. The developed approaches can be used for monitoring and managing water quality.

Keywords: mathematical modelling, organic pollutant, dissolved oxygen, nonlinear differential equation, inverse problem.

UDC: 504.064+519.6

MSC: 65L09, 65L08, 37C60

Received: 14.02.2025

DOI: 10.14529/mmp250204