Some Results on Weak KAM Theory for Time-periodic Tonelli Lagrangian Systems
Some Results on Weak KAM Theory for Time-periodic Tonelli Lagrangian Systems
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DOI：
10.1515/ans-2013-0406
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发表时间：
2013-11
影响因子：
1.8
通讯作者：
Kaizhi Wang;Yong Li
中科院分区：
文献类型：
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作者：
Kaizhi Wang;Yong Li
摘要 本文对时间周期 Tonelli Lagrangian 系统的弱 KAM 理论做出了一些贡献。王和严[Commun.数学。物理。 309 (2012), 663-691]引入了一种与任何时间周期 Tonelli Lagrangian 相关的新型 Lax-Oleinik 类型算子。首先，使用new算子给出后向弱KAM解的等价定义。然后，利用上述定义，证明了以任意连续函数为初始条件的新算子的渐近行为。最后，对于一类特定的时间周期托内利拉格朗日算子，我们讨论了新算子的收敛速度。
Abstract This paper contributes several results on weak KAM theory for time-periodic Tonelli Lagrangian systems. Wang and Yan [Commun. Math. Phys. 309 (2012), 663-691] introduced a new kind of Lax-Oleinik type operator associated with any time-periodic Tonelli Lagrangian. Firstly, using the new operator we give an equivalent definition of the backward weak KAM solution. Then we prove a result on the asymptotic behavior of the new operators with an arbitrary continuous function as initial condition, by taking advantage of the definition mentioned above. Finally, for a specific class of time-periodic Tonelli Lagrangians, we discuss the rate of convergence of the new operators.