# American Institute of Mathematical Sciences

## Instability of free interfaces in premixed flame propagation

 1 School of Mathematical Sciences, Tongji University, 1239 Siping Rd., Shanghai 200092, China 2 Institut de Mathématiques de Bordeaux, Université de Bordeaux, 33405 Talence Cedex, France 3 Plesso di Matematica, Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, Parco Area delle Scienze 53/A, I-43124 Parma, Italy

* Corresponding author: claude-michel.brauner@u-bordeaux.fr

Dedicated to Michel Pierre on his 70th birthday, in friendship.

Received  December 2019 Revised  February 2020 Published  May 2020

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.

Citation: Claude-Michel Brauner, Luca Lorenzi. Instability of free interfaces in premixed flame propagation. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020363
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