RACP2024: Recent advances in Control Theory of PDE systems

From February 12 – 15, 2024 Prof. Enrique Zuazua will talk on Inverse design for conservation laws and Hamilton-Jacobi equations at the “Recent advances in Control Theory of PDE systems” program organized on February 12-23, 2024 by Shirshendu Chowdhury (IISER Kolkata, India), Debayan Maity (TIFR CAM, India) and Debanjana Mitra (IIT Bombay, India).

This program is focused on recent outstanding developments on controllability and stabilizability of parabolic, hyperbolic and dispersive PDEs. These PDEs appear naturally as mathematical models in numerous applications in physics, engineering, biology, and medicine.

Inverse design for conservation laws and Hamilton-Jacobi equations


Inverse time design (Day 01: Feb. 12, 2024)

Flow control in the presence of shocks (Day 02: Feb. 13, 2024)

Inverse design for conservation laws and Hamilton-Jacobi equations (Day 03: Feb. 14, 2024)

Inverse design of one-dimensional Burgers equation (Day 04: Feb. 15, 2024)

Watch the recording of this lecture (YouTube)

Abstract. Some classical nonlinear semigroups arising in mechanics induce unilateral bounds on solutions. Hamilton-Jacobi equations and 1-d scalar conservation laws are classical examples of such nonlinear effects: solutions spontaneously develop one sided Lipschitz or semi-concavity conditions.When this occurs the range of the semigroup is unilaterally bounded by a threshold. On the other hand, in practical applications, one is often led to consider the problem of time-inversion, so to identify the initial sources that originated the observed dynamics at the final time. In these lectures we shall discuss this problem and address the following specific questions:
– Identification of the range of the semigroup.
– Identification of the class of initial data leading to a target.
– Least-square approaches versus backward-forward resolution.
– Numerical reconstruction.
We shall also present a number of open problems arising in this area and the possible link with reinforcement learning.

February 12 – 15, 2024 at 16:00H (local time)

On-site / Online
Ramanujan Lecture Hall

|| This event has been originally shared at: https://dcn.nat.fau.eu/events/racp2024/

Check the program at the official page of the event: https://www.icts.res.in/program/RACP2024