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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 184815, 14 pages
doi:10.1155/2012/184815
Optimal Harvesting for an Age-Spatial-Structured Population Dynamic Model with External Mortality
1Institute of Liberal Education, Catholic University of Daegu, Gyeongsan-si, Gyeongbuk 712-702, Republic of Korea
2Department of Mathematics, Pusan National University, Busan 609-735, Republic of Korea
Received 18 September 2012; Accepted 26 November 2012
Academic Editor: Gue Lee
Copyright © 2012 Yong Han Kang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study an optimal harvesting for a nonlinear age-spatial-structured population dynamic model, where the dynamic system contains an external mortality rate depending on the total population size. The total mortality consists of two types: the natural, and external mortality and the external mortality reflects the effects of external environmental causes. We prove the existence and uniqueness of solutions for the population dynamic model. We also derive a sufficient condition for optimal harvesting and some necessary conditions for optimality in an optimal control problem relating to the population dynamic model. The results may be applied to an optimal harvesting for some realistic biological models.