Existence of measure-valued solutions in optimal control of age-structured populations. Issue 5 (24th March 2023) - Hritonenko, Natali; Kato, Nobuyuki; Yatsenko, Yuri
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.