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Computational Study of Traveling Wave Solutions of Isothermal Chemical Systems

Part of: Chemistry Qualitative theory

Published online by Cambridge University Press:  17 May 2016

Yuanwei Qi  and
Yi Zhu
Yuanwei Qi*
Affiliation:
Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA
Yi Zhu*
Affiliation:
Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA
*
*Corresponding author. Email addresses:yuanwei.qi@ucf.edu (Y. Qi), zhu_y@knights.ucf.edu (Y. Zhu)
*Corresponding author. Email addresses:yuanwei.qi@ucf.edu (Y. Qi), zhu_y@knights.ucf.edu (Y. Zhu)
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Abstract

This article studies propagating traveling waves in a class of reaction-diffusion systems which model isothermal autocatalytic chemical reactions as well as microbial growth and competition in a flow reactor. In the context of isothermal autocatalytic systems, two different cases will be studied. The first is autocatalytic chemical reaction of order m without decay. The second is chemical reaction of order m with a decay of order n, where m and n are positive integers and m>n≥1. A typical system in autocatalysis is A+2B→3B and B→C involving two chemical species, a reactant A and an auto-catalyst B and C an inert chemical species.

The numerical computation gives more accurate estimates on minimum speed of traveling waves for autocatalytic reaction without decay, providing useful insight in the study of stability of traveling waves.

For autocatalytic reaction of order m = 2 with linear decay n = 1, which has a particular important role in chemical waves, it is shown numerically that there exist multiple traveling waves with 1, 2 and 3 peaks with certain choices of parameters.

Keywords

Isothermal chemical systemsmicrobial growth in a flow reactortraveling wavemultiple peak solutionsminimum speedexistencenon-existence

MSC classification

Secondary: 34C20: Transformation and reduction of equations and systems, normal forms 34C25: Periodic solutions 92E20: Classical flows, reactions, etc.
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 5 , May 2016 , pp. 1461 - 1472
Copyright
Copyright © Global-Science Press 2016 

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