Journal
NATURAL RESOURCE MODELING
Volume 22, Issue 2, Pages 173-211Publisher
WILEY
DOI: 10.1111/j.1939-7445.2008.00033.x
Keywords
Optimal fishery harvesting; fisheries management; elliptic partial differential equations; variational inequality
Funding
- National Science Foundation (NSF) [ITR:0427471, MSBS:0532378]
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We consider an optimal fishery harvesting problem using a spatially explicit model with a semilinear elliptic PDE, Dirichlet boundary conditions, and logistic population growth. We consider two objective functionals: maximizing the yield and minimizing the cost or the variation in the fishing effort (control). Existence, necessary conditions, and uniqueness for the optimal harvesting control for both cases are established. Results for maximizing the yield with Neumann (no-flux) boundary conditions are also given. The optimal control when minimizing the variation is characterized by a variational inequality instead of the usual algebraic characterization, which involves the solutions of an optimality system of nonlinear elliptic partial differential equations. Numerical examples are given to illustrate the results.
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