8 papers
Optimal bounds for the cost of fast controls of a KdV system
Hoai-Minh Nguyen
We study the cost of fast controls for a linearized KdV system and a nonlinear KdV system locally, using right Neumann boundary control for non-critical lengths. Since the operator…
Optimal bounds for the boundary control cost of one-dimensional fractional Schrödinger and heat equations
Hoai-Minh Nguyen
We derive sharp bounds for the boundary control cost of the one-dimensional fractional Schrödinger and heat equations. The analysis of the lower bound is based on the study of the…
Characterizations of the Sobolev norms and the total variation via nonlocal functionals, and related problems
Hoai-Minh Nguyen
We briefly discuss the contribution of Haïm Brezis and his co-authors on the characterizations of the Sobolev norms and the total variation using non-local functionals. Some ideas…
Turnpike property of linear quadratic control problems with unbounded control operators
Hoai-Minh Nguyen, Emmanuel Trélat
We establish the turnpike property for linear quadratic control problems for which the control operator is admissible and may be unbounded, under quite general and natural assumpti…
A short introduction to the control theory in finite-dimensional spaces
Hoai-Minh Nguyen
This is a brief introduction to control theory in finite-dimensional spaces. The material is partly based on my lectures for the Master 1 program in Mathématiques et applications a…
One dimensional wave equation with in-domain localized damping and Wentzell boundary conditions
Abdelhakim Dahmani, Yacine Chitour, Hoai-Minh Nguyen +1
This paper is devoted to the exponential stability for one-dimensional linear wave equations with in-domain localized damping and several types of Wentzell (or dynamic) boundary co…