6 papers
Asymptotic observable symmetry for spacetime observability of waves I: The disc
Shengquan Xiang
Building on the spacetime observable symmetry discovered in NWX (2025), we introduce asymptotic observable symmetry (AOS) for the wave equation. Its central object is a family of g…
Observable symmetry for spacetime observability of wave equations on the interval
Bin Huang, Shengquan Xiang
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 cond…
Stability of a Korteweg--de Vries equation close to critical lengths
Jingrui Niu, Shengquan Xiang
In this paper, we investigate the quantitative exponential stability of the Korteweg-de Vries equation on a finite interval with its length close to the critical set. Sharp decay e…
Symmetry conditions for spacetime observability of wave equations on the torus
Jingrui Niu, Ming Wang, Shengquan Xiang
We study observability for the one-dimensional wave equation on the torus from spacetime measurable observation sets. While the Geometric Control Condition (GCC) provides a suffici…
The periodic KdV with control on space-time measurable sets
Jingrui Niu, Ming Wang, Shengquan Xiang
In this paper, we establish the local exact controllability of the KdV equation on torus around equilibrium states, where both the spatial control region and the temporal control r…
Small-time local controllability of a KdV system for all critical lengths
Jingrui Niu, Shengquan Xiang
In this paper, we consider the small-time local controllability problem for the KdV system on an interval with a Neumann boundary control. In 1997, Rosier discovered that the linea…