A necessary and sufficient condition for convergence of the Lax-Oleinik semigroup for reversible Hamiltonians on R-n
A necessary and sufficient condition for convergence of the Lax-Oleinik semigroup for reversible Hamiltonians on R-n
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R-n上可逆哈密顿量Lax-Oleinik半群收敛的充要条件
DOI：
10.1016/j.jde.2016.08.001
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发表时间：
2016
影响因子：
2.4
通讯作者：
Yan Jun
中科院分区：
文献类型：
--
作者：
Liu Qihuai;Wang Kaizhi;Wang Lin;Yan Jun
本文研究了可逆哈密顿算子H （x, p）在R n上的Lax-Oleinik半群的收敛性，给出了该半群收敛的充分必要条件。我们还给出了一个例子，证明了对于R n上的不可逆哈密顿量，即使哈密顿量是可积的，并且初始数据是Lipschitz连续有界的，相应的Lax-Oleinik半群也可能不收敛。
This paper is devoted to the study of the convergence of the Lax–Oleinik semigroup associated with reversible Hamiltonians H (x, p) on R n. We provide a necessary and sufficient condition for the convergence of the semigroup. We also give an example to show that for irreversible Hamiltonians on R n, even if the Hamiltonian is integrable and the initial data is Lipschitz continuous and bounded, the corresponding Lax–Oleinik semigroup may not converge.