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5 postes ATER en mathématiques à Sorbonne Université
date limite le 5 avril à 16h
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189 personnes travaillent au LJLL

90 permanents

82 chercheurs et enseignants-chercheurs permanents

8 ingénieurs, techniciens et personnels administratifs

99 personnels non permanents

73 doctorants

14 post-doc et ATER

12 émérites et collaborateurs bénévoles

 

Chiffres mars 2019

 

Séminaire du LJLL : P. Cannarsa

20 février 2015 — 14h00

Piermarco Cannarsa (Université de Rome 2 Tor Vergata)

Dynamique singulière pour les équations d’Hamilton-Jacobi

Abstract

 In dynamic programming, the set of points at which the value function of an optimal control problem fails to be differentiable is usually regarded as a region to keep away from. Indeed, the uniqueness of optimal trajectories is generally lost on such a set and numerical schemes become less reliable. Such a viewpoint, however, could be partly reversed thinking of the huge quantity of data that can be compressed at a singular point. This talk will be focussed on singularities of solutions to Hamilton-Jacobi equations, in connection with optimal control problems, and the dynamics that describes their propagation. We will be particularly interested in the study of the invariance of the singular set under such dynamics for two examples of solutions to eikonal-type equations : the euclidean (and riemannian) distance function from the boundary of a bounded domain and the solution of a Cauchy problem given by the Hopf-Lax formula.