On the mathematical model of the concentration of pollutants and their impact on the population of the river

Abstract

To study the influence of environmental pollutants on the dynamics of river populations, we present a process-oriented model that elucidates the interplay between a population and toxic substances in a flowing environment. Here, an unknown boundary defines the front for the spread of the toxicant in the aquatic environment. Some properties of the solution are studied, and the global solvability of the problem is established. To solve problems with a free boundary, we establish Schauder-type estimates. The behaviour of a free boundary has been studied.

Keywords

• Model with free boundary
• Toxicant
• Reaction–diffusion–advection equations
• A priori estimates