Keywords

traveling wave, autocatalytic cubic reaction, partial differential equations

Abstract

This thesis studies the traveling wavefront created by the autocatalytic cubic chemical reaction A + 2B → 3B involving two chemical species A and B, where A is the reactant and B is the auto-catalyst. The diffusion coefficients for A and B are given by DA and DB. These coefficients differ as a result of the chemical species having different size and/or weight. Theoretical results show there exist bounds, v* and v*, depending on DB/DA, where for speeds v ≥ v*, a traveling wave solution exists, while for speeds v < v*, a solution does not exist. Moreover, if DB ≤ DA, and v* and v* are similar to one another and in the order of DB/DA when it is small. On the other hand, when DA ≤ DB there exists a minimum speed vmin, such that there is a traveling wave solution if the speed v > vmin. The determination of vmin is very important in determining the dynamics of general solutions. To fill in the gap of the theoretical study, we use numerical methods to determine vmin for various cases. The numerical algorithm used is the fourth-order Runge-Kutta method (RK4).

Notes

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Graduation Date

2008

Advisor

Qi, Yuanwei

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematical Science

Format

application/pdf

Identifier

CFE0002061

URL

http://purl.fcla.edu/fcla/etd/CFE0002061

Language

English

Release Date

June 2008

Length of Campus-only Access

None

Access Status

Masters Thesis (Open Access)

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Included in

Mathematics Commons

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