Harvesting in diffusive population models (mentor: Dr. R. Shivaji)

harvesting The proposed project involves modeling of population dynamics in the presence of harvesting. This research topic is closely related to the important and fast developing areas of natural resource management and bioeconomics. Among many other applications in these areas is the fishery management. An example can be found in some recent articles in the Science magazine describing the fascinating migratory abilities of the Atlantic bluefin tunas (Thunnus thynnus). See also USA TODAY article Thursday, May 15 2003, 11D (See the left Figure.). Despite a history of harvesting and exploitation spanning hundreds of years, little is known about the spatial dynamics of bluefin tuna movement. Inspired by the experimental work of Block et al., to model the spatial dynamics and the mixing of the Atlantic bluefin tunas, Shivaji (Co-PI) and his collaborators have started investigating the reaction-diffusion system,
equation
where $ u(t, x)$ denotes the density of bluefin at time $ t$ at location $ x$ in a bounded region representing the habitat (the Atlantic ocean), $ \Delta $ denotes the Laplacian, the positive parameter $ d$ is the rate of mixing,

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