弯曲流光电离锋的移动边界近似：可解性分析
Moving boundary approximation for curved streamer ionization fronts: Solvability analysis
摘要：
研究了负流光电离锋的最小密度模型。这个模型的早期移动边界近似由Hele-Shaw型拉普拉斯增长问题中的“动力学过冷”型边界条件组成。在这里，我们推导出一个类似于表面张力的移动边界近似的曲率修正。该计算是基于非常规功能的可解性分析，即，有三个相关的零模式的伴随算子，其中一个发散;此外，内/外匹配前面的前面必须执行一条线上，而不是在一个扩展的区域;和整个计算可以解析地执行。分析揭示了前面和后面的缓慢演变的弯曲的前面，曲率和所产生的电导率的字段之间的关系。这种关系迫使我们放弃理想电导率近似，我们建议用一个常数电导率近似来代替它。这意味着，在流光内部的电势不再是恒定的，但解决了拉普拉斯方程，这导致了一个马斯喀特型问题。
英文摘要：
The minimal density model for negative streamer ionization fronts is investigated. An earlier moving boundary approximation for this model consisted of a "kinetic undercooling" type boundary condition in a Laplacian growth problem of Hele-Shaw type. Here we derive a curvature correction to the moving boundary approximation that resembles surface tension. The calculation is based on solvability analysis with unconventional features, namely, there are three relevant zero modes of the adjoint operator, one of them diverging; furthermore, the inner/outer matching ahead of the front has to be performed on a line rather than on an extended region; and the whole calculation can be performed analytically. The analysis reveals a relation between the fields ahead and behind a slowly evolving curved front, the curvature and the generated conductivity. This relation forces us to give up the ideal conductivity approximation, and we suggest to replace it by a constant conductivity approximation. This implies that the electric potential in the streamer interior is no longer constant but solves a Laplace equation; this leads to a Muskat-type problem.
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