Existence of measure-valued solutions in optimal control of age-structured populations. Issue 5 (24th March 2023)

• Record Type: Journal Article
• Authors: Hritonenko, Natali; Kato, Nobuyuki; Yatsenko, Yuri
• Is Part Of: Applicable analysis. Volume 102:Issue 5(2023)
• Page Start: 1281
• Page End: 1293
• Publication Date: 2023-03-24
• Subjects: Optimal harvesting -- age-structured population -- measure -- bounded variation -- distributional partial derivatives; 49J20 -- 92D25; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1981876
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : We consider a nonlinear profit maximization problem in the Lotka–McKendrick model of age-structured harvested population describing farmed populations in agriculture and aquaculture. The control functions are time- and age-dependent harvesting rate and time dependent supply of newborns. We establish the existence of optimal controls with measure-valued harvesting rate by using distributional partial derivatives of functions of bounded variation through the equivalent integrated form to the original problem.