This paper studies the behavior of solutions near the explosion time to the chordal Komatu–Loewner equation for slits, motivated by the preceding studies by Bauer and Friedrich (Math Z 258:241–265, 2008) and by Chen and Fukushima (Stoch Process Appl 128:545–594, 2018). The solution to this equation represents moving slits in the upper half-plane. We show that the distance between the slits and driving function converges to zero at its explosion time. We also prove a probabilistic version of this asymptotic behavior for stochastic Komatu–Loewner evolutions under some natural assumptions.

中文翻译：

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服从狭缝运动的有限爆炸时间服从弦式Komatu-Loewner方程

本文是根据鲍尔和弗里德里希（Math Z 258：241–265，2008）和陈和福岛（Stoch Process Appl，2008）的先前研究的动机，研究狭缝的弦形Komatu-Loewner方程在爆炸时间附近的解的行为。 128：545–594，2018年）。该方程式的解表示在上半平面中移动的狭缝。我们表明，缝隙和驱动函数之间的距离在爆炸时收敛为零。我们还证明了在某些自然假设下随机Komatu-Loewner演化的这种渐近行为的概率版本。