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Title: On a Nonlocal Reaction-Diffusion Problem Arising from the Modeling of Phytoplankton Growth
Contributor(s): Du, Yihong  (author); Hsu, Sze-Bi (author)
Publication Date: 2010
DOI: 10.1137/090775105
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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.
Publication Type: Journal Article
Source of Publication: SIAM Journal on Mathematical Analysis, 42(3), p. 1035-1333
Publisher: Society for Industrial and Applied Mathematics
Place of Publication: Philadelphia, United States of America
ISSN: 0036-1410
Field of Research (FOR): 010110 Partial Differential Equations
Socio-Economic Outcome Codes: 970101 Expanding Knowledge in the Mathematical Sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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Appears in Collections:Journal Article
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