We consider a specific parameter regime in a model for combustion in hydraulically resistant porous media. We prove the existence of the traveling fronts in this regime and investigate their stability. The existence is proved using Geometric Singular Perturbation theory. The stability analysis involves locating the spectrum of the linearization of the underlying system about the front by numerical computation of the Evans function combined with energy-like estimates. Furthermore, a conclusion about nonlinear stability is also obtained.

中文翻译：

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火焰在多孔介质中的传播

我们在抗水力多孔介质中的燃烧模型中考虑了特定的参数范围。我们证明了该政权中存在战线，并对其稳定性进行了研究。利用几何奇异摄动理论证明了该存在。稳定性分析包括通过将Evans函数的数值计算与类似能量的估计相结合来定位底层系统线性化的频谱。此外，还得出了关于非线性稳定性的结论。