EXISTENCE OF WEAK SOLUTION FOR MEAN CURVATURE FLOW WITH TRANSPORT TERM AND FORCING TERM

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EXISTENCE OF WEAK SOLUTION FOR MEAN CURVATURE FLOW WITH TRANSPORT TERM AND FORCING TERM

机译：运输术语和矫正术语平均曲率流动弱解的存在

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We study the mean curvature flow with given non-smooth transport term and forcing term, in suitable Sobolev spaces. We prove the global existence of the weak solutions for the mean curvature flow with the terms, by using the modified Allen-Cahn equation that holds useful properties such as the monotonicity formula.

机译：在合适的SoboLev空间中，我们研究了给定的非平滑运输术语和强制术语的平均曲率流。我们通过使用修改的艾伦-CAHN方程，通过使用诸如单调性公式的有用特性的改性艾伦-CAHN方程来证明平均曲率流动的全局解决方案。

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《Communications on pure and applied analysis》 |2020年第5期|共23页
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正文语种 eng
中图分类数学;
关键词
Mean curvature flow; Allen-Cahn equation; phase field method; varifold; singular limit;

机译：平均曲率流动;艾伦 - CAHN方程;相场法;volifold;奇异限制;

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专利

1. EXISTENCE OF WEAK SOLUTION FOR MEAN CURVATURE FLOW WITH TRANSPORT TERM AND FORCING TERM [J] . Communications on pure and applied analysis . 2020,第5期

机译：运输术语和矫正术语平均曲率流动弱解的存在
2. GRADIENT ESTIMATES AND EXISTENCE OF MEAN CURVATURE FLOW WITH TRANSPORT TERM [J] . Keisuke Takasao Differential and integral equations . 2013,第1a2期

机译：具有运输期限的平均曲率流的梯度估计和存在
3. On the existence of mean curvature flow with transport term [J] . Chun Liu, Norifumi Sato, Yoshihiro Tonegawa Interfaces and free boundaries . 2010,第2期

机译：关于带有运输项的平均曲率流的存在
4. Existence of Nonoscillatory Solutions of Second Order Nonlinear Neutral Difference Equations with a Forced Term [C] . Yonggui Kao, Cunchen Gao, Yongxu Wang ICIHDS 2007;International conference on impulsive and hybrid dynamical systems . 2007

机译：具有强迫项的二阶非线性中立型差分方程非振动解的存在性
5. Convex solutions to the power-of-mean curvature flow, conformally invariant inequalities and regularity results in some applications of optimal transportation. [D] . Chen, Shibing. 2013

机译：平均功率曲率流的凸解，保形不变的不等式和规则性导致最佳运输的某些应用。
6. Global existence of Dirac-wave maps with curvature term on expanding spacetimes [O] . Volker Branding, Klaus Kröncke -1

机译：扩展时空上曲率项的狄拉克波图的整体存在
7. On time-periodic solutions for a weakly anisotropic curvature flow equation with driving force term (Viscosity Solutions of Differential Equations and Related Topics) [O] . Giga Yoshikazu, Ishimura Naoyuki, Kohsaka Yoshihito 2003

机译：具有驱动力项的弱各向异性曲率流方程的时间周期解（微分方程和相关主题的粘度解）

EXISTENCE OF WEAK SOLUTION FOR MEAN CURVATURE FLOW WITH TRANSPORT TERM AND FORCING TERM

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