2025/02/09 by Alberto Bressan, Bressan, Alberto, Elsa M. Marchini +3
Computer Science · #49Q10 #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2502.05968
openalex publication_date 2025/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper is concerned with a family of geometric evolution problems, modeling the spatial control of an invasive population within a region V⊂ \R2 bounded by geographical barriers. If no control is applied, the contaminated set Ω(t)⊂ V expands with unit speed in all directions. By implementing a control, a region of area M can be cleared up per unit time. Given an initial set Ω(0)=Ω0⊆ V, three main problems are studied: (1) Existence of an admissible strategy t↦Ω(t) which eradicates the contamination in finite time, so that Ω(T)=∅ for some T>0. (2) Optimal strategies that achieve eradication in minimum time. (3) Strategies that minimize the average area of the contaminated set on a given time interval [0,T]. For these optimization problems, a sufficient condition for optimality is proved, together with several necessary conditions. Based on these conditions, optimal set-valued motions t↦ Ω(t) are explicitly constructed in a number of cases. \endabstract