In this paper we analyze the stability of the traveling wave solution for an ignition-temperature first-order reaction model of diffusional-thermal combustion in the case of high Lewis numbers ($\mathrm{Le}>1$). In contrast to conventional Arrhenius kinetics where the reaction zone is infinitely thin, the reaction zone for stepwise temperature kinetics is of order unity. The system of two parabolic PDEs is characterized by a free interface at which ignition temperature ${\mathrm{\Theta }}_i$ is reached. We turn the model to a fully nonlinear problem in a fixed domain. When the Lewis number is large, we define a bifurcation parameter $m={\mathrm{\Theta }}_i/(1-{\mathrm{\Theta }}_i)$ and a perturbation parameter $\epsilon =1/\mathrm{Le}$. The main result is the existence of a critical value $m^c(\epsilon )$ close to $m^c=6$ at which Hopf bifurcation holds for ε small enough. Proofs combine spectral analysis and non-standard application of Hurwitz's Theorem with asymptotics as $\epsilon \to 0$.

在高Lewis数的情况下，我们分析了扩散热燃烧的点火温度一阶反应模型的行波解的稳定性（$\mathrm{乐}>\mathrm{1个}$）。与反应区无限薄的常规Arrhenius动力学相反，逐步温度动力学的反应区具有统一的数量级。两个抛物线型PDE的系统的特征是在点火温度下有一个自由界面${\mathrm{\Theta }}_{\mathrm{一世}}$到达了。我们将模型转换为固定域中的完全非线性问题。当Lewis数很大时，我们定义一个分叉参数$米={\mathrm{\Theta }}_{\mathrm{一世}}/（\mathrm{1个}-{\mathrm{\Theta }}_{\mathrm{一世}}）$ 和一个扰动参数 $\epsilon =\mathrm{1个}/\mathrm{乐}$。主要结果是存在临界值${米}^C（\epsilon ）$ 相近 ${米}^C=6$Hopf分叉处的ε足够小。证明将频谱分析和Hurwitz定理的非标准应用与渐近性结合起来$\epsilon \to 0$。