20 citations · 43 across the 13 of their papers we have counts for
15 papers
Controlled harmonic map heat flow and blow-up from the disk to the sphere
Shengquan Xiang
We study the one-corotational harmonic map heat flow from the disk to the sphere with a Dirichlet boundary control. We introduce a control-adapted gluing strategy to prevent blow-u…
Wave maps from circle to Riemannian manifold: global controllability is equivalent to homotopy
Jean-Michel Coron, Joachim Krieger, Shengquan Xiang
We study wave maps from the circle to a general compact Riemannian manifold. We prove that the global controllability of this geometric equation is characterized precisely by the h…
Global controllability to harmonic maps of the heat flow from a circle to a sphere
Jean-Michel Coron, Shengquan Xiang
In this paper, we study the global controllability and stabilization problems of the harmonic map heat flow from a circle to a sphere. Combining ideas from control theory, heat flo…
Global controllability and stabilization of the wave maps equation from a circle to a sphere
Jean-Michel Coron, Joachim Krieger, Shengquan Xiang
Continuing the investigations started in the recent work [Krieger-Xiang, 2022] on semi-global controllability and stabilization of the -dimensional wave maps equation with s…
Semi-global controllability of a geometric wave equation
Joachim Krieger, Shengquan Xiang
We prove the semi-global controllability and stabilization of the -dimensional wave maps equation with spatial domain and target . First we show…
Fredholm backstepping for critical operators and application to rapid stabilization for the linearized water waves
Ludovick Gagnon, Amaury Hayat, Shengquan Xiang +1
Fredholm-type backstepping transformation, introduced by Coron and Lü, has become a powerful tool for rapid stabilization with fast development over the last decade. Its strength l…
Stability of multi-population traffic flows
Amaury Hayat, Benedetto Piccoli, Shengquan Xiang
Traffic waves, known also as stop-and-go waves or phantom hams, appear naturally as traffic instabilities, also in confined environments as a ring-road. A multi-population traffic…
On the global approximate controllability in small time of semiclassical 1-D Schrödinger equations between two states with positive quantum densities
Jean-Michel Coron, Shengquan Xiang, Ping Zhang
In this paper, we study, in the semiclassical sense, the global approximate controllability in small time of the quantum density and quantum momentum of the 1-D semiclassical cubic…
Fredholm transformation on Laplacian and rapid stabilization for the heat equation
Ludovick Gagnon, Amaury Hayat, Shengquan Xiang +1
We study the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. We prove that, under some assumption…
Stabilization of the linearized water tank system
Jean-Michel Coron, Amaury Hayat, Shengquan Xiang +1
In this article we study the so-called water tank system. In this system, the behavior of water contained in a 1-D tank is modelled by Saint-Venant equations, with a scalar distrib…
Small-time local stabilization of the two dimensional incompressible Navier-Stokes equations
Shengquan Xiang
We provide explicit time-varying feedback laws that locally stabilize the two dimensional internal controlled incompressible Navier-Stokes equations in arbitrarily small time. We a…
Quantitative rapid and finite time stabilization of the heat equation
Shengquan Xiang
The null controllability of the heat equation is known for decades [19,23,30]. The finite time stabilizability of the one dimensional heat equation was proved by Coron--Nguyên [13]…
Boundary stabilization of focusing NLKG near unstable equilibria: radial case
Joachim Krieger, Shengquan Xiang
We investigate the stability and stabilization of the cubic focusing Klein-Gordon equation around static solutions on the closed ball of radius L in . First we show t…
Cost for a controlled linear KdV equation
Joachim Krieger, Shengquan Xiang
The controllability of the linearized KdV equation with right Neumann control is studied in the pioneering work of Rosier [25]. However, the proof is by contradiction arguments and…
Local exponential stabilization for a class of Korteweg-de Vries equations by means of time-varying feedback laws
Jean-Michel Coron, Ivonne Rivas, Shengquan Xiang
We study the exponential stabilization problem for a nonlinear Korteweg-de Vries equa- tion on bounded interval in cases where the linearized control system is not controllable. Th…