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### Open Access Journals

CPAA

In 1953, G.I. Taylor published his paper concerning the transport of a
contaminant in a fluid flowing through a narrow tube. He demonstrated that
the transverse variations in the fluid's velocity field and the transverse
diffusion of the solute interact to yield an effective longitudinal mixing
mechanism for the transverse average of the solute. This mechanism has
been dubbed ``Taylor Dispersion.'' Since then, many related studies have
surfaced. However, few of these addressed the effects of nonlinear chemical reactions upon a system of solutes undergoing Taylor
Dispersion. In this paper, I present a mathematical model for the evolution
of the transverse averages of reacting solutes in a fluid flowing down a pipe
of arbitrary cross-section. The technique for deriving the model is a generalization
of an approach by introduced by P.C. Fife. The key outcome is
that while one still finds an effective mechanism for longitudinal mixing,
there is also a effective mechanism for nonlinear advection.

CPAA

The carbonate system is an important reaction system in natural
waters because it plays the role of a buffer, regulating the pH of the water. We
present a global existence result for a system of partial differential equations
that can be used to model the combined dynamics of diffusion, advection, and
the reaction kinetics of the carbonate system.

DCDS

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.

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.

CPAA

We study the global existence and qualitative properties of the solutions of
nonlinear parabolic systems. Such systems commonly arise in situations
pertaining to reactive transport. Particular examples include the modeling of
chemical reactions in rivers or in blood streams.

In this paper, we first establish a maximum principle that generates

In this paper, we first establish a maximum principle that generates

*a-priori*bounds for solutions to a broad class of parabolic systems. Afterward, we develop an alternative technique for establishing global bounds on solutions to a specific system of three equations that belong to a*different*class of parabolic systems. Finally, we prove that the only bounded traveling wave solutions to this system are constants.## Year of publication

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