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Title: Effects of a Degeneracy in the Competition Model Part I.: Classical and Generalized Steady-State Solutions
Contributor(s): Du, Y (author)
Publication Date: 2002
DOI: 10.1006/jdeq.2001.4074
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Abstract: We study the competition model where the coefficient functions are strictly positive over the underlying spatial region Ω except b(x), which vanishes in a nontrivial subdomain of Ω, and is positive in the rest of Ω. We show that there exists a critical number λ* such that if λ <λ*, then the model behaves similarly to the well-studied classical competition model where all the coefficient functions are positive constants, but when λ>λ*, new phenomena occur. Our results demonstrate the fact that heterogeneous environmental effects on population models are not only quantitative, but can be qualitative as well. In part I here, we mainly study two kinds of steady-state solutions which determine the dynamics of the model: one consists of finite functions while the other consists of generalized functions which satisfy (u, v)=(∞, 0) on the part of the domain that b(x) vanishes, but are positive and finite on the rest of the domain, and are determined by certain boundary blow-up systems. The research is continued in part II, where these two kinds of steady-state solutions will be used to determine the dynamics of the model.
Publication Type: Journal Article
Source of Publication: Journal of Differential Equations, 181(1), p. 92-132
Publisher: Academic Press
Place of Publication: United States
ISSN: 0022-0396
Field of Research (FOR): 010110 Partial Differential Equations
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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