THE GLOBAL LIPSCHITZ SOLUTION FOR A PEELING MODEL*

doi:10.1007/s10473-023-0519-3

数学物理学报 ›› 2023, Vol. 43 ›› Issue (5): 2263-2278.doi: 10.1007/s10473-023-0519-3

THE GLOBAL LIPSCHITZ SOLUTION FOR A PEELING MODEL^*

Qianfeng Li^1,2†, Yongqian Zhang²

1. School of Mathematical Sciences and Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai 200241, China;
2. School of Mathematical Sciences, Fudan University, Shanghai 200433, China

收稿日期:2021-09-28 修回日期:2023-04-26 出版日期:2023-10-26 发布日期:2023-10-25

THE GLOBAL LIPSCHITZ SOLUTION FOR A PEELING MODEL^*

Qianfeng Li^1,2†, Yongqian Zhang²

1. School of Mathematical Sciences and Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai 200241, China;
2. School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received:2021-09-28 Revised:2023-04-26 Online:2023-10-26 Published:2023-10-25
Contact: †Qianfeng Li, E-mail: qfli@math.ecnu.edu.cn
About author:Yongqian Zhang, yongqianz@fudan.edu.cn
Supported by:
Li’s research was supported by the NSFC (12271507) and the Science and Technology Commission of Shanghai Municipality (22DZ2229014). Zhang’s research was supported by the NSFC (12271507).

摘要/Abstract

摘要： This paper focusses on a peeling phenomenon governed by a nonlinear wave equation with a free boundary. Under the hypotheses that the total variation of the intial data and the boundary data are small, the global existence of a weak solution to the nonlinear problem (1.1)-(1.3) is proven by a modified Glimm scheme. The regularity of the peeling front is established, and the asymptotic behaviour of the obtained solution and the peeling front at infinity is also studied.

关键词: peeling model, nonlinear wave solution, free boundary, Glimm scheme

Abstract: This paper focusses on a peeling phenomenon governed by a nonlinear wave equation with a free boundary. Under the hypotheses that the total variation of the intial data and the boundary data are small, the global existence of a weak solution to the nonlinear problem (1.1)-(1.3) is proven by a modified Glimm scheme. The regularity of the peeling front is established, and the asymptotic behaviour of the obtained solution and the peeling front at infinity is also studied.

Key words: peeling model, nonlinear wave solution, free boundary, Glimm scheme

中图分类号:

35L70

Qianfeng Li, Yongqian Zhang. THE GLOBAL LIPSCHITZ SOLUTION FOR A PEELING MODEL^*[J]. 数学物理学报, 2023, 43(5): 2263-2278.

Qianfeng Li, Yongqian Zhang. THE GLOBAL LIPSCHITZ SOLUTION FOR A PEELING MODEL^*[J]. Acta mathematica scientia,Series A, 2023, 43(5): 2263-2278.

参考文献

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THE GLOBAL LIPSCHITZ SOLUTION FOR A PEELING MODEL^*

THE GLOBAL LIPSCHITZ SOLUTION FOR A PEELING MODEL^*

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