Date: Mon. March 8, 2021
Organized by: Chair in Applied Analysis – Alexander von Humboldt Professorship at FAU Erlangen-Nürnberg
Title: Unilateral bounds for nonlinear semigroups and time-inversion

Speaker: Our Head Prof. Dr. Enrique Zuazua
Affiliation: FAU Erlangen-Nürnberg, Germany

On March 8th, our Head Enrique Zuazua talked on the ‘Geometric and functional inequalities and applications’ Seminar Series about: Unilateral bounds for nonlinear semigroups and time-inversion

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 led to consider the problem of time-inversion, so to identify the initial sources that have led to the observed dynamics at the final time.

In this lecture we shall discuss this problem answering to the following two questions: On one hand, to identify the range of the semigroup and, given a target, to characterize and reconstruct the ensemble of initial data leading to it. Illustrative numerical simulations will be presented, and a complete geometric interpretation will also be provided. We shall also present a number of open problems arising in this area and the possible link with reinforcement learning.

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