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Local maxima of solutions to some nonsymmetric reaction‐diffusion systems
Author(s) -
Nakagawa Junichi,
Nakamura Gen,
Sasayama Satoshi,
Wang Haibing
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2838
Subject(s) - arrhenius equation , reaction–diffusion system , scaling , mathematics , diffusion , sintering , term (time) , maxima , chemical equation , hot spot (computer programming) , diffusion process , process (computing) , thermodynamics , statistical physics , mathematical analysis , chemistry , geometry , physics , activation energy , computer science , organic chemistry , art , knowledge management , innovation diffusion , quantum mechanics , performance art , art history , operating system
In this study, we examine the solution profile of some reaction‐diffusion systems. The systems are derived after approximating the Arrhenius term in our system which models the sintering process and consists of two coupled equations in terms of two unknowns. The unknowns describe the temperature of the solid and the concentration of the fuel. We show the evolution over time of local temperature hot spots. The key idea is to use ‘microscopic scaling’ around the temperature hot spot at the initial time along with asymptotic analysis. We also provide some numerical results that support the efficiency of our analysis. Copyright © 2013 John Wiley & Sons, Ltd.