Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The success of fast reaction: a discrete reaction-diffusion model

Author: Matthias Büger
Journal: Quart. Appl. Math. 62 (2004), 623-641
MSC: Primary 35K57; Secondary 34C11, 35Q80, 37N25, 91B28, 92D15
DOI: https://doi.org/10.1090/qam/2104265
MathSciNet review: MR2104265
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Abstract: We discuss the dynamics of a system of $ 2n$ ordinary differential equations that can be looked at as the discrete version of a system of two reaction--diffusion equations, which differ only in their sensitivity to the reaction term. Such reaction--diffusion systems occur in evolutionary models from biology. It is known that only the fastest reacting species survives in generic situations. We prove similar results for the related discrete system and give an interpretation of the results in terms of mathematical finance.

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DOI: https://doi.org/10.1090/qam/2104265
Article copyright: © Copyright 2004 American Mathematical Society

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