DOI: 10.1007/s00245-005-0847-9 Appl Math Optim 54:1–15 (2006) © 2006 Springer Science+Business Media, Inc. Optimal Harvesting in an Age-Structured Predator–Prey Model ∗ K. Renee Fister 1 and Suzanne Lenhart 2 1 Department of Mathematics and Statistics, Murray State University, Murray, KY 42071-3341, USA renee.fister@murraystate.edu 2 Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, USA lenhart@math.utk.edu and Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6016, USA Communicated by D. Kinderlehrer Abstract. We investigate optimal harvesting control in a predator–prey model in which the prey population is represented by a first-order partial differential equa- tion with age-structure and the predator population is represented by an ordinary differential equation in time. The controls are the proportions of the populations to be harvested, and the objective functional represents the profit from harvesting. The existence and uniqueness of the optimal control pair are established. Key Words. Optimal control, Age-structure, Predator–prey. AMS Classification. 49K20, 35F20. 1. Introduction We consider optimal harvesting control in a predator–prey model in which only the prey population has age-structure. The life cycle of the predator is deemed significantly longer ∗ The research of the first author was partially supported by the Kentucky NSF EPSCoR Research Enhancement Grant #9874764 and the AWM Collaborative Research Grant. The research of the second author was partially supported by the National Science Foundation Grant EF-ITR 0427471.