TY - JOUR
T1 - Optimal solutions for a class of set-valued evolution problems
AU - Bianchini, Stefano
AU - Bressan, Alberto
AU - Chiri, Maria Teresa
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
PY - 2025/1
Y1 - 2025/1
N2 - The paper is concerned with a class of optimization problems for moving sets t↦Ω(t)⊂R2, motivated by the control of invasive biological populations. Assuming that the initial contaminated set Ω0 is convex, we prove that a strategy is optimal if an only if at each given time t∈[0,T] the control is active along the portion of the boundary ∂Ω(t) where the curvature is maximal. In particular, this implies that Ω(t) is convex for all t≥0. The proof relies on the analysis of a one-step constrained optimization problem, obtained by a time discretization.
AB - The paper is concerned with a class of optimization problems for moving sets t↦Ω(t)⊂R2, motivated by the control of invasive biological populations. Assuming that the initial contaminated set Ω0 is convex, we prove that a strategy is optimal if an only if at each given time t∈[0,T] the control is active along the portion of the boundary ∂Ω(t) where the curvature is maximal. In particular, this implies that Ω(t) is convex for all t≥0. The proof relies on the analysis of a one-step constrained optimization problem, obtained by a time discretization.
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U2 - 10.1007/s00526-024-02888-1
DO - 10.1007/s00526-024-02888-1
M3 - Article
AN - SCOPUS:85211328441
SN - 0944-2669
VL - 64
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 1
M1 - 24
ER -