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Local maxima of solutions to some nonsymmetric reaction‐diffusion systems |
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| Authors: | Junichi Nakagawa Gen Nakamura Satoshi Sasayama Haibing Wang |
| Institution: | 1. Mathematical Sciences & Technology Research Laboratories, Advanced Technology Research Laboratories, Nippon Steel & Sumitomo Metal Corporation, , Futsu 293‐8511, Japan;2. Department of Mathematics, Inha University, , Incheon 402‐751, South Korea;3. Department of Mathematics, Hokkaido University, , Sapporo 060‐0810, Japan;4. Department of Mathematics, Southeast University, , Nanjing 210096, China |
| Abstract: | 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. |
| Keywords: | reaction‐diffusion system local maximum microscopic scaling |