区间上波动方程时空可观测性的可观测对称性
Observable symmetry for spacetime observability of wave equations on the interval
- School of Mathematical Sciences, Peking University（北京大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究一维区间波动方程在Dirichlet和Neumann边界条件下的时空可观测性，证明可观测对称性条件与几何控制条件共同构成可观测性的充要条件，并给出唯一延拓性质的充要条件。
AI中文摘要：
继文献[27]之后，我们进一步研究一维区间上波动方程的时空可观测性。主要任务是在Dirichlet和Neumann两种边界条件下刻画可观测对称性条件（OSC），由于边界反射的存在，该问题比环面情形更为复杂，并讨论不同设置下OSC之间的关系。我们证明OSC与几何控制条件（GCC）共同构成可观测性的充要条件。我们还给出了相关唯一延拓性质的充要条件。
英文摘要：
Following the work [27], we further study spacetime observability for the wave equation on a one-dimensional interval. The main task is to characterize the observable symmetry condition (OSC) under both Dirichlet and Neumann boundary conditions, which is more complex than the torus setting due to boundary reflection, and to discuss the relation between OSC under different settings. We prove that OSC, together with the geometric control condition (GCC), is necessary and sufficient for observability. We also provide a necessary and sufficient condition for the related unique continuation property.
