The boundness of the operator-valued functions for multidimensional nonlinear wave equations with applications
The boundness of the operator-valued functions for multidimensional nonlinear wave equations with applications
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DOI：
10.1016/j.aml.2017.04.026
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发表时间：
2017-12
期刊：
影响因子：
--
通讯作者：
Changying Liu;Xinyuan Wu
中科院分区：
文献类型：
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作者：
Changying Liu;Xinyuan Wu
算子变分常数公式是由Wu等人推导的。（2015），并证明了该公式适用于不同的边界条件。此外，Liu等人还提出了一种求解一维非线性周期边界条件Hamilton波动方程的能量守恒格式。（2016年）。已知该公式与依赖于拉普拉斯算子的算子值函数相关联。因此，证明算子值函数的有界性至关重要。这激发了对算子值函数有界性的新的研究。作为应用，我们将能量守恒格式从一维推广到多维非线性哈密顿波动方程，并给出了三种不同的边界条件。
The operator-variation-of-constants formula was derived by Wu et al. (2015) for the general multidimensional nonlinear wave equations, and the authors proved that the formula is adapted to different boundary conditions. Furthermore, an energy-preserving scheme for one-dimensional (1D) nonlinear Hamiltonian wave equations with periodic boundary conditions was proposed by Liu et al. (2016). It is known that the formula is associated with the operator-valued functions which depend on Laplacian. Hence, it is crucial to show the boundness of the operator-valued functions. This motivates the new study of the boundness of the operator-valued functions. As an application, we extend the energy-preserving scheme from 1D to multidimensional nonlinear Hamiltonian wave equations with three different boundary conditions.