We address a problem of boundary control for nonlinear scalar conservation law. Namely, this article is devoted to the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE) with triangular flux function evolving along single road. The target state time- and space-dependent trajectory. law constructed using analytical solution Hamilton–Jacobi (H–J) equation, which an integral form...

The unidirectional acoustic boundary has a broad application prospect. Besides the acoustic metamaterial or the strongly nonlinear acoustic medium, which were applied in the realization of the unidirectional acoustic boundary, the present paper proposes another approach through the active control method, where the control source has the property of single directivity. In order to validate its e...

This paper studies the local exact controllability and the local stabilization of the semilinear Schrödinger equation posed on a product of n intervals (n ≥ 1). Both internal and boundary controls are considered, and the results are given with periodic (resp. Dirichlet or Neumann) boundary conditions. In the case of internal control, we obtain local controllability results which are sharp as fa...

The general problem under consideration in this paper is the stability analysis of hyperbolic systems. Some sufficient criteria on the boundary conditions exist for the stability of a system of conservation laws. We investigate the problem of the stability of such a system in presence of boundary errors that have a small C1-norm. Two types of perturbations are considered in this work: the error...

This article is devoted to analyze control properties for the heat equation with singular potential −μ/|x| arising at the boundary of a smooth domain Ω ⊂ R , N ≥ 1. This problem was firstly studied by Vancostenoble and Zuazua [18] and then generalized by Ervedoza [8] in the context of interior singularity. Roughly speaking, these results showed that for any value of parameters μ ≤ μ(N) := (N − ...

We present some results concerning the controllability of a quasi-linear parabolic equation (with linear principal part) in a bounded domain of RN with Dirichlet boundary conditions. We analyze the controllability problem with distributed controls (supported on a small open subset) and boundary controls (supported on a small part of the boundary). We prove that the system is null and approximat...

This paper concerns second order sufficient conditions of optimality, involving the Riccati equation, for optimal control problems with periodic boundary conditions. The problems considered involve no pathwise constraints and are ‘regular’, in the sense that the strengthened Legendre-Clebsch condition is assumed to be satisfied. A well-known sufficient condition, which we refer to as the Riccat...

We study a 2D and a 3D incompressible magnetohydrodynamic (MHD) channel flow, also known as Hartmann flow, which is electrically conducting and subject to an external transverse magnetic field. We consider periodic boundary condition along one axis (two axis, for the three-dimensional case). We consider the flow at low magnetic Reynolds number and obtain the so-called simplified magnetohydrodyn...