The first part will be devoted to a concise introduction to combustion theory and modeling. Flames constitute an intricate physical system involving fluid dynamics and multistep chemical kinetics. Asymptotic methods introduced by the Russian school in the early mid-20th century allow significant simplifications, especially when a thin flame zone is replaced by a free interface, the flame front.  Flame theory has provided a rich range of equations with fascinating mathematical properties, such as the Kuramoto-Sivashinsky equation.

In a second part, I will briefly discuss a recent work with Lina Hu, Jie Shen and Gregory Sivashinsky on a gas-solid combustion model which generates fingering pattern formation [1]. If time permits, I will give a quick overview of a two-interface problem studied with Peter Gordon and Wen Zhang [2].

[1]  L. Hu, C.-M Brauner, J. Shen, G.I. Sivashinsky, Modeling and simulation of fingering pattern formation in a combustion model, M3AS, 5(2015), pp. 685-720.

[2]  C.-M Brauner, P. Gordon, W. Zhang, An ignition-temperature model with two free interfaces in premixed flames, Combution Theory Modelling (2016). http://dx.doi.org/10.1080/13647830.2016.1220625.