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）

地点：致远楼101室

时间：2019年5月7日 16:00

摘要：

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[4]). Then, we may reformulate the systems as fully nonlinear problems [6] which are very suitable for local existence [4], stability analysis [1,3,5] and numerical simulation [2].

Some references:

[1] D. Addona, C.-M B., L. Lorenzi, W. Zhang, Instabilities in a combustion model with two free interfaces. arXiv:1807.02462.

[2] C.-M B., P. Gordon, W. Zhang, An ignition-temperature model with two free interfaces in premixed flames, Combustion Theory Model., 20(2016), 976-994. (Dedicated to G.I. Sivashinsky).

[3] C.-M. B., J. Hulshof and A. Lunardi,A general approach to stability in free boundary problems, J. Differential Equations 164 (2000), 16-48.

[4] C.-M. B. and L. Lorenzi, Local existence in free interface problems with underlying second-order Stefan condition, Rom. J. Pure Appl. Math. (23)2018, 339-359. (Dedicated to P. G. Ciarlet).

[5] C.-M B., L. Lorenzi, M.M. Zhang, Stability analysis and Hopf bifurcation for large Lewis number in a combustion model with free interface. arXiv:1901.01123.

[6] A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhauser, Basel, 1996.

欢迎各位参加！