Unilateral bounds for nonlinear semigroups and time-inversion by E. Zuazua
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
March 8th, 2021 at 15:00H (GMT Central European time)
Request the Zoom link to email@example.com
Enrique Zuazua Alexander von Humboldt Professorship | Head of the Chair of Computational Mathematics | Professor of Applied MathematicsEnrique ZuazuaAlexander von Humboldt Professorship | Head of the Chair of Computational Mathematics | Professor of Applied Mathematics
Enrique Zuazua (Eibar, Basque Country – Spain, 1961) holds an Alexander von Humboldt Professorship at the Friedrich–Alexander University (FAU), Erlangen (Germany). He is also the Director of the Chair of Computational Mathematics at Deusto Foundation, Universidad de Deusto (Bilbao, Basque Country-Spain) where he leads the research team funded by the ERC Advanced Grant DyCoN project. He is also a Professor of Applied Mathematics since 2001 at the Department of Mathematics of the Autonomous University of Madrid where he holds a Strategic Chair.
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