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Asymptotic behaviour, uniqueness and stability of coexistence states of a non-cooperative reaction–diffusion model of nuclear reactors

Published online by Cambridge University Press:  04 February 2010

Rui Peng ,
Dong Wei  and
Guoying Yang
Rui Peng
Affiliation:
Institute of Nonlinear Complex Systems, College of Science, China Three Gorges University, Yichang City, 443002 Hubei Province, People's Republic of China, and School of Science and Technology, University of New England, Armidale, NSW 2351, Australia, (pengrui_seu@163.com)
Dong Wei
Affiliation:
Hebei University of Engineering, Handan, Hebei 056038, People's Republic of China, (wdongau@yahoo.com.cn)
Guoying Yang
Affiliation:
Department of Mathematics, Henan Polytechnic University, Jiaozuo City 45400, People's Republic of China, (ygyhfyg@yahoo.com.cn)
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Abstract

We investigate a non-cooperative reaction-diffusion model arising in the theory of nuclear reactors and are concerned with the associated steady-state problem. We determine the asymptotic behaviour of the coexistence states near the point of bifurcation from infinity, which exhibits the following very interesting spatial blow-up pattern: when the fuel temperature reaches a certain value, the free fast neutrons undergoing nuclear reaction will blow up in each spatial point of the interior of the reactor. Without any restriction on spatial dimensions, we also discuss the uniqueness and stability of the coexistence states. Our results complement and sharpen those derived in two recent works by Arioli and Lóopez-Gómez.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 1 , February 2010 , pp. 189 - 201
Copyright
Copyright © Royal Society of Edinburgh 2010

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