Existence of measure-valued solutions in optimal control of age-structured populations

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.

Keywords:

• Optimal harvesting
• age-structured population
• measure
• bounded variation
• distributional partial derivatives

2010 Mathematics Subject Classifications:

• 49J20
• 92D25

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by JSPS KAKENHI [grant number JP17K05273].