SINGULAR LIMIT ANALYSIS OF STABILITY OF TRAVELING-WAVE SOLUTIONS IN BISTABLE REACTION-DIFFUSION SYSTEMS
SINGULAR LIMIT ANALYSIS OF STABILITY OF TRAVELING-WAVE SOLUTIONS IN BISTABLE REACTION-DIFFUSION SYSTEMS
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DOI：
10.1137/0521006
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发表时间：
1990-01-01
影响因子：
2
通讯作者：
FUJII, H
中科院分区：
文献类型：
--
作者：
NISHIURA, Y;MIMURA, M;FUJII, H
研究了一类扩散速率和反应速率均存在较大差异的反应扩散方程组行波解的稳定性.与标量系统不同，该系统在适当的参数范围内存在多个行波。每个波可以通过使用奇异摄动方法来构造，并且其稳定性或不稳定性由其构造中出现的简单代数量确定：即，内外匹配条件的雅可比矩阵的符号。本文所采用的奇异极限方法（与形式极限方法有很大的不同）是严格的，在研究奇摄动解的稳定性问题中是非常有用的。
The stability properties of the traveling front solutions to bistable reaction-diffusion systems in which there are big differences in both the diffusion rates and the reaction rates between two species are studied. In contrast to the scalar case, this bistable system has multiple existence of traveling waves in the appropriate region of parameters. Each wave can be constructed by using a singular perturbation method, and its stability or instability is determined by a simple algebraic quantity appearing in its construction: namely, the sign of the Jacobian of inner and outer matching conditions. The singular limit approach (which is quite different from formal limiting arguments) adopted in this paper is rigorous and very useful in the study of stability problems of singularly perturbed solutions.