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https://hdl.handle.net/1959.11/457
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 | Handle Link: | https://hdl.handle.net/1959.11/457 | 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="then" the="the" model="model" behaves="behaves" similarly="similarly" to="to" well-studied="well-studied" classical="classical" competition="competition" where="where" all="all" coefficient="coefficient" functions="functions" are="are" positive="positive" constants="constants" but="but" when="when" λ="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.λ> | Publication Type: | Journal Article | Source of Publication: | Journal of Differential Equations, 181(1), p. 92-132 | Publisher: | Academic Press | Place of Publication: | United States of America | ISSN: | 1090-2732 0022-0396 |
Fields of Research (FoR) 2008: | 010110 Partial Differential Equations | 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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