On a 2D transmission problem with singularity at the interface modeling autoignition of reactive jets. (English) Zbl 1543.35094
Summary: We consider a traveling wave solution of a two-dimensional transmission problem across the \(y\)-axis modeling autoignition of reactive jets, with 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 a problem in a distributional sense that verifies the transmission system and closely examine the properties of the solution near the singularity. Using the Implicit Function Theorem, we study the level sets, especially the one through the origin. The numerical illustrations are consistent with our theoretical results.
MSC:
| 35K57 | Reaction-diffusion equations |
| 35C07 | Traveling wave solutions |
| 35A21 | Singularity in context of PDEs |
| 35A08 | Fundamental solutions to PDEs |
| 33C10 | Bessel and Airy functions, cylinder functions, \({}_0F_1\) |
| 80A25 | Combustion |
Keywords:
transmission problem; fixed interface; traveling waves; singularity; fundamental solution; Bessel functions; autoignitionReferences:
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