Unilateral bounds for nonlinear semigroups and time-inversion
On March 8th, our Head Enrique Zuazua will be talking 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.
TO ATTEND TO THIS TALK Missed this? Find the recording below!
March 8th, 2021 at 15:00H (UTC / 09:00H EST)
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