论文标题
关于二维域中波动方程的凯奇问题，边界上有数据
On the Cauchy problem for the wave equation in a two-dimensional domain with data on the boundary
论文作者
论文摘要
本文的主题是时空气缸中的cauchy问题，$ω\ times {\ mathbb r} $，$ω\ subset {\ mathbb r}^2 $，并在表面$ \partialΩ\partialΩ\ times i $上，其中$ i $是一个有限的时间间隔。以前获得了有关$ s \ times i $，$ s \ subset \partialΩ$的数据解决库奇问题的算法。在这里，我们将此算法调整到特殊情况下$ s = \partialΩ$，并表明在这种情况下，与情况相比，该解决方案的稳定性较高，而与情况相比$ s \ subsetneqq \partialΩ$。
The subject of the paper is the Cauchy problem for the wave equation in a space-time cylinder $Ω\times{\mathbb R}$, $Ω\subset{\mathbb R}^2$, with the data on the surface $\partialΩ\times I$, where $I$ is a finite time interval. The algorithm for solving the Cauchy problem with the data on $S\times I$, $S\subset\partialΩ$, was obtained previously. Here we adapt this algorithm to the special case $S=\partialΩ$ and show that in this situation, the solution is determined with higher stability in comparison with the case $S\subsetneqq\partialΩ$.
