Abstract and Applied Analysis
Volume 2012 (2012), Article ID 184815, 14 pages
http://dx.doi.org/10.1155/2012/184815
Research Article

Optimal Harvesting for an Age-Spatial-Structured Population Dynamic Model with External Mortality

Yong Han Kang,1 Mi Jin Lee,2 and Il Hyo Jung2

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.