TY - JOUR
T1 - On the slit motion obeying chordal Komatu–Loewner equation with finite explosion time
AU - Murayama, Takuya
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2020/3/1
Y1 - 2020/3/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00028-019-00519-3
DO - 10.1007/s00028-019-00519-3
M3 - Article
AN - SCOPUS:85066973329
VL - 20
SP - 233
EP - 255
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
SN - 1424-3199
IS - 1
ER -