CIRM-FBK 2021: Inverse design for conservation laws and Hamilton-Jacobi equations by E. Zuazua

On Friday September 24, our Head Enrique Zuazua will talk on “Inverse design for conservation laws and Hamilton-Jacobi equations” at the CIRM-FBK event 2021 on “Analysis, Control and Numerics for PDE Models of interest to physical and life Sciences” in Levico Terme (Trento, Italy), sponsored by CIRM – Centro Internazionale per la Ricerca Matematica, FBK – Fondazione Bruno Kessler, INdAM and UNITN.

Speaker: Prof. Dr. Enrique Zuazua
Affiliation: FAU Erlangen – Nürnberg (Germany)

WHEN?

Fri. September 24, 2021 at 09:00H (GMT + 2)

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 this lecture 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.

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