Existence of measure-valued solutions in optimal control of age-structured populations
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.
Hritonenko, N., Kato, N., & Yatsenko, Y. (2021). Existence of measure-valued solutions in optimal control of age-structured populations. Retrieved from https://digitalcommons.pvamu.edu/mathematics-facpubs/1