Reaction Diffusion Equations Arising from Phytoplankton Dynamics

Abstract

Partial differential equation theory, especially the theory of reaction-diffusion equations, has long been found extremely useful in the qualitative study of theoretical ecology. The interplay between partial differential equations and mathematical ecology not only benefits ecology greatly, it is also one of the important sources from which many beautiful and challenging mathematical models have been derived and henceforth helps to develop the theory of partial differential equations. In this thesis, we are concerned with the mathematical study of a basic model proposed by ecologists describing the ecological behaviors of phytoplankton in eutrophic environments. The model is viewed by some ecologists as a very realistic model to describe the behavior of phytoplankton. On the other hand, the model involves a nonlocal term and is mathematically challenging, and not much mathematical research has been carried out on it. This thesis is an attempt to further the understanding of this model.