学术报告

报告题目：Free interface problemsarising inpremixedflame propagation  

报告人：Claude-MichelBrauner，(波尔多大学教授)  

报告时间：6月22 日上午11:00—11:45  

报告地点：数统院307  

                                          数学与统计学院

                                             2019.6.20

报告摘要：In combustion theory, the propagation of premixedflames is usually described bythe conventional thermal-diffusional model withstandard Arrhenius kinetics. Formalasymptotic methods based on large activation energyhave allowed simpler descriptions,especially when the thin flame zone isreplaced by a free interface, called the flame front,which separates burned andunburned gases. At the flame front, the temperature andmass fraction gradientsare discontinuous.    

Modelsdescribing dynamics of thick flames with stepwise ignition-temperature kineticshave recently received considerable attention. There are dierences with theArrheniuskinetics, for example in the case of zero-order stepwise kinetics there aretwo free interfaces. At the free interface(s), the temperature and massfraction gradients are this timecontinuous.    

Bothfree interface problems (Arrhenius and ignition-temperature kinetics) do notfallwithinthe class of Stefan problems, as there is no specific condition on the velocityof theinterface(s).However, at least near planar traveling fronts, we are able to associate thevelocity with acombination of spatial derivatives up to the second order (second-orderStefan 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-temperaturemodel 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.