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Modeling chemical reactions in rivers: A three component reaction. (English) Zbl 1010.80013

Summary: 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 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.

MSC:

80A32 Chemically reacting flows
35K57 Reaction-diffusion equations
35B35 Stability in context of PDEs
86A05 Hydrology, hydrography, oceanography
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