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https://hdl.handle.net/1959.11/7469
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 | Handle Link: | https://hdl.handle.net/1959.11/7469 | 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: | United States of America | ISSN: | 1095-7154 0036-1410 |
Fields of Research (FoR) 2008: | 010110 Partial Differential Equations | Socio-Economic Objective (SEO) 2008: | 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 School of Science and Technology |
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