Global Solutions of the Asymptotically Periodic Curvature Flow Equations in Band Domains

LIU Qian; CHEN Ruiqi

doi:10.21656/1000-0887.410087

Volume 42 Issue 2

Feb. 2021

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LIU Qian, CHEN Ruiqi. Global Solutions of the Asymptotically Periodic Curvature Flow Equations in Band Domains[J]. Applied Mathematics and Mechanics, 2021, 42(2): 180-187. doi: 10.21656/1000-0887.410087

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Global Solutions of the Asymptotically Periodic Curvature Flow Equations in Band Domains

doi: 10.21656/1000-0887.410087

LIU Qian¹,
CHEN Ruiqi²

¹Department of Foundation Courses, Guangdong Polytechnic of Environmental Protection Engineering, Foshan, Guangdong 528216, P.R.China;²Mathematics & Science College, Shanghai Normal University,Shanghai 200030, P.R.China

Funds: The National Natural Science Foundation of China（11671262）

Received Date: 2020-03-27
Rev Recd Date: 2020-07-31
Publish Date: 2021-02-01

Abstract

Abstract

The curvature flow equations were studied with Neumann boundary conditions and asymptotically periodic coefficients. First, a series of initial value problems and corresponding global solutions were considered. By uniform prior estimates, a subsequence converging to the global solution was obtained. Second, the uniqueness of the global solution was proved with the renormalization method in the direction of negative infinite time and the strong maximum principle. Finally, to study the ω-limit and α-limit of the global solution, the renormalization method was used again. Through the construction of the pullback function, the uniform prior estimation and the convergent subsequence with the Cantor diagonalization method, it is shown that, the ω-limit and α-limit of global solutions are the global solutions of the corresponding limit problems, i.e., they both are periodic traveling waves.
- mean curvature flow,
- asymptotically periodic function,
- global solution,
- periodic traveling wave

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References(17)

References

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