Title

The Development Of Travelling Waves In Cubic Auto-Catalysis With Different Rates Of Diffusion

Keywords

Cubic auto-catalysis; Minimum speed; Reaction-diffusion; Travelling wave

Abstract

In this paper we study the isothermal auto-catalytic chemical reaction, A + 2 B → 3 B involving two chemical species A and B. Their diffusion coefficients, denoted by DA and DB, respectively, are unequal, which happens when the two chemical species have different molecular weights. The propagating reaction-diffusion waves that may develop from a local initial input of the auto-catalyst, B, are investigated in one spatial dimension. We show the existence of travelling wave solutions for all propagation speed v ≥ v2*, with v2* a function of the ratio of the diffusion rates of the species A and B, representing the estimated minimum propagation speed. Our result improves significantly on the results of early works. In addition, we show the non-existence of travelling wave solutions when v ≤ v2, where v2 depends on the ratio of the diffusion rates of the species A and B. We believe that our non-existence result is the first of the kind for equations of the isothermal auto-catalytic chemical reaction type. We also demonstrate similar results on the general isothermal auto-catalytic chemical reaction, A + n B → (n + 1) B, of n-th order with n > 1. © 2006 Elsevier Ltd. All rights reserved.

Publication Date

2-15-2007

Publication Title

Physica D: Nonlinear Phenomena

Volume

226

Issue

2

Number of Pages

129-135

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.physd.2006.11.010

Socpus ID

33846590412 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/33846590412

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