Modeling chemical reactions in rivers: A three component reaction

Abstract

What follows is the analysis of a model for dynamics of chemical reactions in a river. Dominant forces to be considered include diffusion, advection, and rates of creation or destruction of participating species (due to chemical reactions). In light of this, the model we will be using will be based upon a nonlinear system of reaction-advection-diffusion equations. The nonlinearity comes solely from the influences of the chemical reactions. First, we will establish some general results for reaction diffusion systems. In particular, we will illustrate a class of reaction diffusion systems whose solutions are bounded from below by zero. We will also provide a local existence result for this class of problems. Afterwards, we will focus on the dynamics of an equidiffusive three component reaction system. Specifically, we will provide conditions under which one could be guaranteed the existence of global solutions. We will also discuss the qualities of the $\omega$-limit set for this system.