On the slit motion obeying chordal Komatu–Loewner equation with finite explosion time

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Abstract

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.

Original languageEnglish
Pages (from-to)233-255
Number of pages23
JournalJournal of Evolution Equations
Volume20
Issue number1
DOIs
Publication statusPublished - Mar 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

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