具有常平均曲率的$H$-表面热流的有限时间爆破

IF 0.7 4区数学 Q2 MATHEMATICS

Annales Polonici Mathematici Pub Date : 2021-04-04 DOI:10.4064/ap210403-26-7

Haixia Li

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引用次数: 0

摘要

本文考虑了Huang等人在[论常平均曲率曲面方程的热流，Mathematica, 2011, 134: 259-271]中研究的常平均曲率曲面方程热流的初边值问题，得到了正则解的全局适定性和有限时间爆破性。本文对他们的结果进行了补充，为求解有限时间奇点提供了一些新的条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Finite time blow-up for the heat flow of $H$-surface with constant mean curvature

Abstract In this paper, the authors consider an initial boundary value problem for the heat flow of equation of surfaces with constant mean curvatures, which was investigated in [On the heat flow of equation of surfaces of constant mean curvatures, Manuscripta Mathematica, 2011, 134: 259-271] by Huang et al., where global well-posedness and finite time blow-up of regular solutions were obtained. Their results are complemented in this paper in the sense that some new conditions on the initial data are provided for the solutions to develop finite time singularity.

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来源期刊

Annales Polonici Mathematici 数学-数学

CiteScore

0.90

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： Annales Polonici Mathematici is a continuation of Annales de la Société Polonaise de Mathématique (vols. I–XXV) founded in 1921 by Stanisław Zaremba. The journal publishes papers in Mathematical Analysis and Geometry. Each volume appears in three issues.