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Publications in Scientific Journals:

D. Grass, H. Uecker, T. Upmann:
"Optimal fishery with coastal catch";
Natural Resource Modeling, 1 (2019), 12235; 32 pages.



English abstract:
In many spatial resource models, it is assumed that an
agent is able to harvest the resource over the complete
spatial domain. However, agents frequently only have
access to a resource at particular locations at which a
moving biomass, such as fish or game, may be caught or
hunted. Here, we analyze an infinite time‐horizon
optimal control problem with boundary harvesting and
(systems of) parabolic partial differential equations as
state dynamics. We formally derive the associated
canonical system, consisting of a forward-backward
diffusion system with boundary controls, and numerically
compute the canonical steady states and the
optimal time‐dependent paths, and their dependence
on parameters. We start with some one‐species fishing
models, and then extend the analysis to a predator-prey
model of the Lotka-Volterra type. The models are rather
generic, and our methods are quite general, and thus
should be applicable to large classes of structurally
similar bioeconomic problems with boundary controls.

Keywords:
bioeconomics, bistable model, infinite time horizon, optimal boundary control, optimal harvesting, Pontryagin´s maximum principle, predator-prey model


Electronic version of the publication:
https://publik.tuwien.ac.at/files/publik_281248.pdf


Created from the Publication Database of the Vienna University of Technology.