In this survey, we are interested in the instability of flame fronts regarded as free interfaces. We successively consider a classical Arrhenius kinetics (thin flame) and a stepwise ignition-temperature kinetics (thick flame) with two free interfaces. A general method initially developed for thin flame problems subject to interface jump conditions is proving to be an effective strategy for smoother thick flame systems. It relies on the elimination of the free interface(s) and reduction to a fully nonlinear parabolic problem. The theory of analytic semigroups is a key tool to study the linearized operators.

中文翻译：

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自由界面在预混火焰传播中的不稳定性

在这项调查中，我们对被视为自由界面的火焰锋的不稳定性感兴趣。我们先后考虑了经典的Arrhenius动力学（薄火焰）和具有两个自由界面的逐步点火温度动力学（厚火焰）。最初针对界面跳动条件下的稀薄火焰问题开发的通用方法被证明是使较厚的火焰系统更平滑的有效策略。它依赖于消除自由接口并将其简化为完全非线性的抛物线问题。解析半群理论是研究线性化算子的关键工具。