离散莫尔斯流的Yamabe型热流

Pub Date : 2023-01-01 DOI:10.4208/jpde.v36.n1.3

Ma Li null, Weiqiong Zheng

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引用次数: 0

摘要

．本文研究了整个空间中有界正则域上Yamabe型热流和非线性热流的离散莫尔斯流。我们证明了在初始数据g的适当假设下，在任何时间间隔上的Yamabe型热流都具有弱近似离散莫尔斯流。这种现象与平滑的山边流非常不同，后者可能存在有限时间的爆炸。

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Discrete Morse Flow for Yamabe Type Heat Flows

. In this paper, we study the discrete Morse ﬂow for either Yamabe type heat ﬂow or nonlinear heat ﬂow on a bounded regular domain in the whole space. We show that under suitable assumptions on the initial data g one has a weak approxi-mate discrete Morse ﬂow for the Yamabe type heat ﬂow on any time interval. This phenomenon is very different from the smooth Yamabe ﬂow, where the ﬁnite time blow up may exist.

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