Stability of planar wave solutions to combustion model
Stability of planar wave solutions to combustion model
复制标题
燃烧模型平面波解的稳定性
DOI：
10.1137/0521063
复制
发表时间：
1990
影响因子：
2
通讯作者：
D. Terman
中科院分区：
文献类型：
--
作者：
D. Terman
一个系统的反应扩散方程出现作为一个一步燃烧过程的模型被认为是。主要关注的是这个模型的平面波解的稳定性。这个问题已经从匹配渐近的观点在无限激活能的极限下得到了广泛的研究。渐近分析表明，对于较大的参数范围，平面波解是不稳定的。当某一参数变化时，平面波解可能发生Hopf分叉或稳态分叉。本文对某些渐近结果给出了严格的数学证明。
A system of reaction diffusion equations which arise as a model for a one-step combustion process is considered. The primary concern is with the stability of planar wave solutions to this model. This problem has been studied extensively from the point of view of matched asymptotics in the limit of infinite activation energy. The asymptotic analysis has demonstrated that for a large range of parameters, the planar wave solution is unstable. As a particular parameter is varied, the planar wave solution may undergo either a Hopf or steady state bifurcation. This paper gives a rigorous mathematical justification of some of the asymptotic results.