Mathematical Model For Environmental Pollution Prevention

Abstract

This paper explores mathematical modeling methods based on differential equations aimed at preventing environmental pollution. The main focus is on formalizing the dynamics of pollutant dispersion, degradation, and removal over space and time. To this end, advection-diffusion type partial differential equations (PDEs) are employed, with analytical solutions obtained using separation of variables, as well as numerical approaches. By applying optimal control theory, management functions to reduce pollution in ecological systems are constructed and explained using Pontryagin's maximum principle. Moreover, stochastic differential equations (SDEs) are introduced to account for uncertainties present in real ecological processes, which is of particular importance for ecological risk assessment. The proposed models provide a theoretical foundation for environmental system management while allowing more precise mathematical investigation of applied ecological problems.