报告题目：Free interface problems arising in premixed flame propagation

报 告 人：Claude-Michel Brauner教授（波尔多大学）

报告时间：2019年6月22日  11:00-11:45

报告地点：数统院307学术报告厅

报告摘要：

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 dierences 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 with 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 premixedflames, Combustion Theory Model. 20 (2016), 976-994. (Dedicated to G.I. Sivashinsky).

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

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

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

[6] A. Lunardi, Analytic Semigroups and OptimalRegularity in Parabolic Problems, Birkhäuser, Basel,1996.