Local maxima of solutions to some nonsymmetric reaction‐diffusion systems. (19th June 2013)

• Record Type: Journal Article
• Authors: Nakagawa, Junichi; Nakamura, Gen; Sasayama, Satoshi; Wang, Haibing
• Is Part Of: Mathematical methods in the applied sciences. Volume 37:Number 5(2014:Mar. 30)
• Page Start: 752
• Page End: 767
• Publication Date: 2013-06-19
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.2838
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma2838-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p id="mma2838-para-0001">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 &amp; Sons, Ltd.</p> </abstract>