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• W2048095188 abstract "This paper examines a system of reaction–diffusion equations arising from a flowing water habitat. In this habitat, one or two microorganisms grow while consuming two growth-limiting, complementary (essential) resources. For the single population model, the existence and uniqueness of a positive steady-state solution is proved. Furthermore, the unique positive solution is globally attracting for the system with regard to nontrivial nonnegative initial values. Mathematical analysis for the two competing populations is carried out. More precisely, the long-time behavior is determined by using the monotone dynamical system theory when the semi-trivial solutions are both unstable. It is also shown that coexistence solutions exist by using the fixed point index theory when the semi-trivial solutions are both (asymptotically) stable." @default.
• W2048095188 created "2016-06-24" @default.
• W2048095188 creator A5035933163 @default.
• W2048095188 date "2010-12-01" @default.
• W2048095188 modified "2023-10-18" @default.
• W2048095188 title "A system of partial differential equations modeling the competition for two complementary resources in flowing habitats" @default.
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• W2048095188 doi "https://doi.org/10.1016/j.jde.2010.07.031" @default.
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