题目：Free Interface Problems Arising in Premixed Flame Propagation
报告人：Prof. Claude-Michel Brauner （波尔多大学 数学学院）
In combustion theory, the propagation of premixed flames is usually described by the conventional thermal-diffusional model with standard Arrhenius kinetics. Formal asymptotic methods based on large activation energy have allowed simpler descriptions, especially when the thin flame zone is replaced by a free interface, called the flame front, which separates burned and unburned gases. At the flame front, the temperature and mass fraction gradients are discontinuous.
Models describing dynamics of thick flames with stepwise ignition-temperature kinetics have recently received considerable attention. There are differences with the Arrhenius kinetics, for example in the case of zero-order stepwise kinetics there are two free interfaces. At the free interface(s), the temperature and mass fraction gradients are this time continuous.
Both free interface problems (Arrhenius and ignition-temperature kinetics) do not fall within the class of Stefan problems, as there is no specific condition on the velocity of the interface(s). However, at least near planar traveling fronts, we are able to associate the velocity to a combination of spatial derivatives up to the second order (second-order Stefan condition). Then, we may reformulate the systems as fully nonlinear problems  which are very suitable for local existence , stability analysis [1,3,5] and numerical simulation .
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