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ON A DIFFUSION EQUATION WITH RUPTURE

Giga, Yoshikazu Ueda, Yuki 北海道大学

2023.10.16

概要

1.1. Setting of the problem. We consider a cluster of bubbles which
occupies a domain in a plane R2 whose boundary is the graph of a function
h. We postulate that a bubble touches the graph y = h(x) (from below) on a
fixed horizontal region and that the difference of slopes of adjacent bubbles
is fixed. We further assume that h is periodic with period ω to simplify the
problem. To fix theidea, let Uk denote the k-th
bubble on (ak , ak+1 ) whose
boundary contains y = h(x) ak < x < ak+1 , where {ak }K
k=1 is a division
of [0, ω), i.e., 0 ≤ a1 < a2 < · · · < ω; see Figure 1. The index is taken
modulo K so that a1+K = a1 . ...

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参考文献

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18

YOSHIKAZU GIGA AND YUKI UEDA

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Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba

Meguro-ku, Tokyo 153-8914, Japan

Email address: labgiga@ms.u-tokyo.ac.jp

Research Institute for Electronic Science, Hokkaido University, N12W7, KitaWard Sapporo, Hokkaido 060-0812, Japan

Email address: yukiueda@es.hokudai.ac.jp

...

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