Thibault Liard

Analysis and numerical solvability of backward-forward conservation laws

Thibault Liard, Enrique Zuazua. Analysis and numerical solvability of backward-forward conservation laws (2022) Abstract. In this paper, we study the problem of initial data identification for weak-entropy solutions of the…

Initial data identification for the one-dimensional Burgers equation

Thibault Liard, Enrique Zuazua. Initial data identification for the one-dimensional Burgers equation. (2021). IEEE T Automat. Contr. DOI: 10.1109/TAC.2021.3096921 Abstract. In this paper, we study the problem of identification for…

Analysis and numerics solvability of backward-forward conservation laws

Backward-forward method, Conservation Laws, Identification problems, Non-smooth optimization problem, Wave-front tracking algorithm, Weak-entropy solutions

Thibault Liard, Enrique Zuazua. Analysis and numerics solvability of backward-forward conservation laws. (2020) Abstract. In this paper, we study the problem of initial data identification for the one-dimensional Burgers equation.…

A PDE-ODE model for traffic control with autonomous vehicles

Thibault Liard, Raphael Stern, Maria Laura Delle Monache. A PDE-ODE model for traffic control with autonomous vehicles. (2020) Abstract. We introduce a coupled PDE-ODEs model to describe mixed traffic with…

A controlled multiscale model for traffic regulation via autonomous vehicles

T. Liard, . A controlled multiscale model for traffic regulation via autonomous vehicles. (2019) Abstract. Autonomous vehicles ($AV$s) allow new ways of regulating the traffic flow on road networks. Most…

On entropic solutions to conservation laws coupled with moving bottlenecks

T. Liard, Benedetto Piccoli. On entropic solutions to conservation laws coupled with moving bottlenecks. (2019) Abstract. Moving bottlenecks in road traffic represent an interesting mathematical problem, which can be modeled…

Optimal driving strategies for traffic control with autonomous vehicles

T. Liard, Raphael Stern, Maria Laura Delle Monache. Optimal driving strategies for traffic control with autonomous vehicles. (2019) Abstract. This article considers the possibility of using a small number of…

Inverse design for the one-dimensional Burgers equation

T. Liard, E. Zuazua. Inverse design for the one-dimensional Burgers equation. (2019) Abstract. In this paper, we study the problem of inverse design for the one-dimensional Burgers equation. This problem…

Analysis and numerical solvability of backward-forward conservation laws

Initial data identification for the one-dimensional Burgers equation

Analysis and numerics solvability of backward-forward conservation laws

A PDE-ODE model for traffic control with autonomous vehicles

A controlled multiscale model for traffic regulation via autonomous vehicles

On entropic solutions to conservation laws coupled with moving bottlenecks

Optimal driving strategies for traffic control with autonomous vehicles

Inverse design for the one-dimensional Burgers equation

Nonuniqueness of minimizers for semilinear optimal control problems

The turnpike property and the long-time behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems

A framework for randomized time-splitting in linear-quadratic optimal control

Numerical Control: Part A

Numerical hypocoercivity for the Kolmogorov equation