Control of Three Dimensional Water Waves
Control of Three Dimensional Water Waves
复制标题
三维水波控制
DOI：
--
复制
发表时间：
2017
影响因子：
2.5
通讯作者：
Huixian Zhu
中科院分区：
文献类型：
--
作者：
Huixian Zhu
我们研究了具有表面张力的空间周期性水波的精确可控性，通过局部外部压力施加于自由表面。证明了在任意维度上，只要控制区域满足几何控制条件，对于足够小且规则的数据，在任意短时间内都具有精确的可控性。该结果由Alazard等人（J Eur Math Soc 20(3), 657-745, 2018）在二维水波中得到。我们的证明结合了一个迭代方案，该方案将原始拟线性方程的可控性降低到线性方程序列的可控性，并结合了线性控制问题的半经典方法。
We study the exact controllability for spatially periodic water waves with surface tension, by localized exterior pressures applied to free surfaces. We prove that in any dimension, the exact controllability holds within an arbitrarily short time, for sufficiently small and regular data, provided that the region of control satisfies the geometric control condition. This result was previously obtained by Alazard et al. (J Eur Math Soc 20(3), 657–745, 2018) for 2-D water waves. Our proof combines an iterative scheme, that reduces the controllability of the original quasi-linear equation to that of a sequence of linear equations, with a semiclassical approach for the linear control problems.
具有非局域初始数据的重力水波系统的柯西理论
DOI：
10.48550/arxiv.1305.0457
发表时间：
2013
期刊：
arXiv e-prints
影响因子：
--
作者：
Alazard Thomas
通讯作者：
Alazard Thomas