题目: A 2D transmission problem modeling autoignition with singularity at the interface

报告人：Claude-Michel Brauner (University of Bordeaux)

时间：10月22日（星期四） 14:30

地点：数学新楼308

摘要:

In combustion theory, the spontaneous growth of reaction rates in reactive systems is a classical problem. Mathematical modeling of autoignition traces back to 1920’s-1930’s theory of thermal explosion. It is common that autoignition instantaneously results in flame propagation, however, in contrast to flame fronts, ignition fronts generate weak chemical reactions.

In this talk, we consider a traveling wave solution of a two-dimensional transmission problem across the y-axis modeling autoignition of reactive jets^[3], a limiting version corresponding to large heat loss. A jump of the normal derivative generates a singularity at the origin. We construct an explicit solution to the problem in distributional sense and closely examine the properties of the solution near the singularity. We study the level sets, especially through the origin, see^[1].

Transmission problems were widely studied in the 1950s-1960s, particularly under the influence of M. Picone, J.-L. Lions, G. Stampacchia and M. Schechter. Significant recent work has shown a renewed interest in this area, see L. A. Caffarelli, M. Soria-Carro and P. R. Stinga^[2].

References:

[1] C.-M. Brauner. P. Shang and L. Zhang, On a 2D transmission problem with singularity at the interface modeling autoignition of reactive jets, DCDS-B, 29 (2024), 3446-3470.

[2] L. A. Caffarelli, M. Soria-Carro and P. R. Stinga, Regularity for \(C^{1,\alpha}\) interface transmission problems, Arch. Ration. Mech. Anal., 240 (2021), 265-294.

[3] P. V. Gordon, U. G. Hegde and M. C. Hicks, On traveling front of ignition in co-flow laminar reactive jets, SIAM J. Appl. Math, 81 (2021), 47-59.