Séminaires : Combinatoire, Optimisation, et Interactions

The purpose of this seminar is to foster exchanges within the CO team of IMJ-PRG, and also with the surrounding scientific community. As such, its range of topics should be quite broad. We initially plan one or two sessions per month.

Ce séminaire a pour but de développer les échanges au sein de l'équipe Combinatoire et Optimisation, et avec la communauté scientifique environnante. Ses thèmes seront donc larges. Nous prévoyons un rythme initial de une à deux séances par mois.

The talk is concerned with a family of geometric evolution problems, modeling the spatial control of an invasive population within a plane region bounded by geographical barriers. The "contaminated region" is a set moving in the plane, which we would like to shrink as much as possible.  To control the evolution of this set, we assign the velocity in the inward normal direction at every boundary point. Three main problems are studied: existence of an admissible strategy which eradicates the contamination in finite time,  optimal strategies that achieve eradication in minimum time, strategies that minimize the average area of the contaminated set on a given time interval. For these optimization problems, a sufficient condition for optimality is proved, together with several necessary conditions.  Based on these conditions, optimal  set-valued motions are explicitly constructed in a number of cases.