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On the Heat Flow of Equation of H-Surface

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Abstract

We study the heat flow of equation of H-surface with non-zero Dirichlet boundary in the present article. Introducing the “stable set” \(\mathfrak{M}_2\) and “unstable set” \(\mathfrak{M}_1\), we show that there exists a unique global solution provided the initial data belong to \(\mathfrak{M}_2\) and the global solution converges to zero in H1 exponentially as time goes to infinity. Moreover, we also prove that the local regular solution must blow up at finite time provided the initial data belong to \(\mathfrak{M}_1\).

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Authors and Affiliations

  1. Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, China

    Guochun Wu

  2. School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and Scientific Computing, Xiamen University, Xiamen, 361005, China

    Zhong Tan

  3. College of Information Science and Technology, Hunan Agriculture University, Changsha, 410128, China

    Jiankai Xu

Authors
  1. Guochun Wu
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  2. Zhong Tan
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  3. Jiankai Xu
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Corresponding author

Correspondence to Zhong Tan.

Additional information

Guochun Wu’s research was in part supported by National Natural Science Foundation of China (11701193, 11671086), Natural Science Foundation of Fujian Province (2018J05005), Program for Innovative Research Team in Science and Technology in Fujian Province University Quanzhou High-Level Talents Support Plan (2017ZT012). Zhong Tan’s research was in part supported by National Natural Science Foundation of China (11271305, 11531010). Jiankai Xu’s research was in part supported by National Natural Science Foundation (11671086, 11871208), Natural Science Foundation of Hunan Province (2018JJ2159).

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Wu, G., Tan, Z. & Xu, J. On the Heat Flow of Equation of H-Surface. Acta Math Sci 39, 1397–1405 (2019). https://doi.org/10.1007/s10473-019-0516-8

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  • DOI: https://doi.org/10.1007/s10473-019-0516-8

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