5 papers
Asymptotic observable symmetry for spacetime observability of waves II: Smooth bounded domains
Jingrui Niu, Shengquan Xiang
Continuing \cite{NWX} and Part I \cite{AOSI}, we further investigate symmetry for spacetime observability of wave equations. Building on asymptotic observable symmetry (AOS) introd…
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…