带有耗散项的双曲平均曲率流

数学物理学报 ›› 2026, Vol. 46 ›› Issue (5): 1691-1705.

带有耗散项的双曲平均曲率流

王增桂()

聊城大学数学与系统科学学院山东聊城 252059

收稿日期:2025-07-19 修回日期:2026-03-13 出版日期:2026-10-26 发布日期:2026-09-07
作者简介:王增桂, E-mail:wangzenggui@lcu.edu.cn
基金资助:
山东省自然科学基金(ZR2021MA084);山东省自然科学基金(ZR2026MS0004);聊城大学教改基金(311162387)

Hyperbolic Mean Curvature Flow with A Dissipative Term

Zenggui Wang()

School of Mathematical and Systems Science, Liaocheng University, Shandong Liaocheng 252059

Received:2025-07-19 Revised:2026-03-13 Online:2026-10-26 Published:2026-09-07
Supported by:
Natural Science Foundation of Shandong Province(ZR2021MA084);Natural Science Foundation of Shandong Province(ZR2026MS0004);Teaching Reform Projects of Liaocheng University(311162387)

摘要/Abstract

摘要：

该文研究了一类带有耗散项的双曲平均曲率流. 借助 DeTurk 技巧, 将双曲几何演化方程约化为严格双曲型偏微分方程组. 根据标准的双曲型偏微分方程理论, 证明了解的短时间存在唯一性以及定义在欧式空间上 $\mathbb{R}^{n}(n>2)$ 非线性稳定性. 另外, 推导出几何量如度量和曲率满足的非线性波动方程.

关键词: 带有耗散项的双曲平均曲率流, 局部存在性, 非线性稳定性, 非线性波动方程

Abstract:

Hyperbolic mean curvature flow with a dissipative term is introduced. By a strick of DeTurk, the quasilinear hyperbolic equations can be reduced to the strictly hyperbolic equations. Local existence and uniqueness of the flow is proved. Furthermore, we discuss the nonlinear stability of the flow defined in $\mathbb{R}^{n}(n>2)$. Finally, the evolution equations of metric and curvature are derived.

Key words: hyperbolic mean curvature flow with a dissipative term, local existence, nonlinear stability, nonlinear wave equations

中图分类号:

O175.2

王增桂. 带有耗散项的双曲平均曲率流[J]. 数学物理学报, 2026, 46(5): 1691-1705.

Zenggui Wang. Hyperbolic Mean Curvature Flow with A Dissipative Term[J]. Acta mathematica scientia,Series A, 2026, 46(5): 1691-1705.

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