Mathematical models of interaction between pollutant and environment

Various mathematical models of the interaction between the animate nature and a pollutant are considered. It is known that the animate nature can absorb pollutant up to certain limits (threshold value). Experiments show that the dependence between the emitted quantity of a pollutant and the remaining quantity can be described by a certain function. If some quantity of the pollutant is emitted regularly, we obtain an iterative process for a sequence of functions describing the dependence between the emitted and remaining quantities of the pollutant. We prove that this sequence converges. Using this discrete functional model, we construct a system of two differential equations of Lotka-Volterra types. This, in turn, enables us to build a distributed model on the plane and in three-dimensional space. Taking into account the diffusion of the pollutant and the distribution of plants, we obtain the system of three semi-linear parabolic equations. We present various results of numerical simulation for our distributed model.