On a Nonlocal Reaction-Diffusion Problem Arising from the Modeling of Phytoplankton Growth

Title
On a Nonlocal Reaction-Diffusion Problem Arising from the Modeling of Phytoplankton Growth
Publication Date
2010
Author(s)
Du, Yihong
( author )
OrcID: https://orcid.org/0000-0002-1235-0636
Email: ydu@une.edu.au
UNE Id une-id:ydu
Hsu, Sze-Bi
Type of document
Journal Article
Language
en
Entity Type
Publication
Publisher
Society for Industrial and Applied Mathematics
Place of publication
United States of America
DOI
10.1137/090775105
UNE publication id
une:7637
Abstract
In this paper we analyze a nonlocal reaction-diffusion model which arises from the modeling of competition of phytoplankton species with incomplete mixing in a water column. The nonlocal nonlinearity in the model describes the light limitation for the growth of the phytoplankton species. We first consider the single-species case and obtain a complete description of the long-time dynamical behavior of the model. Then we study the two-species competition model and obtain sufficient conditions for the existence of positive steady states and uniform persistence of the dynamical system. Our approach is based on a new modified comparison principle, fixed point index theory, global bifurcation arguments, elliptic and parabolic estimates, and various analytical techniques.
Link
Citation
SIAM Journal on Mathematical Analysis, 42(3), p. 1035-1333
ISSN
1095-7154
0036-1410
Start page
1035
End page
1333

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