Hyperbolic systems model the phenomena of propagations at finite speeds. They are
present in many fields of science and, consequently, in many human applications. For these …

In this article we study the so-called water tank system. In this system, the behavior of water
contained in a one dimensional tank is modelled by Saint-Venant equations, with a scalar …

We construct explicit time-varying feedback laws leading to the global (null) stabilization in
small time of the viscous Burgers equation with three scalar controls. Our feedback laws use …

This paper addresses the impact of the presence of a boundary memory term in the third-
order Korteweg–de Vries equation in a bounded interval 0, ℓ 0, ℓ. First, an overall literature …

We consider a 1-D linear transport equation on the interval (0, L), with an internal scalar
control. We prove that if the system is controllable in a periodic Sobolev space of order …

We use the backstepping method to study the stabilization of a 1-D linear transport equation
on the interval (0, L), by controlling the scalar amplitude of a piecewise regular function of …

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--Nguy\^ en [13] …

The aim of this work is to study the exponential stability of the nonlinear Korteweg-de Vries
equation in the presence of a delayed internal feedback. We first consider the case where …

In this article, we study the exponential stabilization of some one-dimensional nonlinear
coupled parabolic-ODE systems, namely Rogers–McCulloch and FitzHugh–Nagumo …

We construct explicit time-varying feedback laws that locally stabilize the two-dimensional
internal controlled incompressible Navier–Stokes equations in arbitrarily small time. We also …