Continuing the investigations started in the recent work [12] on semi-global controllability and stabilization of the (1+1)-dimensional wave maps equation with spatial domain S1 and target Sk , where semi-global refers to the 2π-energy bound, we prov ...
We study the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. This classical framework allows us to present the backstepping method with Fredholm transformations for the Lapla ...
We prove the semi-global controllability and stabilization of the (1+1)−dimensional wave maps equation with spatial domain 𝕊1 and target Sk. First we show that damping stabilizes the system when the energy is strictly below the threshold 2π, where ha ...
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 distributed control. It is well-known that the linearized systems around uniform st ...
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 the value of the observability constant remains unknown, though rich mathem ...
