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https://hdl.handle.net/1959.11/3460
Title: | Realization of prescribedpatterns in the competition model | Contributor(s): | Du, Yihong (author) | Publication Date: | 2003 | DOI: | 10.1016/S0022-0396(03)00056-1 | Handle Link: | https://hdl.handle.net/1959.11/3460 | Abstract: | We demonstrate that for any prescribed set of finitely many disjoint closed subdomains D₁,...,Dm of a given spatial domain Ω in R^N, if d₁,d₂,a₁,a₂,c,d,e are positive continuous functions on Ω and b(x) is identically zero on D:=D₁∪...∪Dm and positive in the rest of Ω, then for suitable choices of the parameters λ, μ and all small ε>0, the competition model u₁(x,t)-d₁(x)Δu(x,t)=λa₁(x)u-[ε⁻¹b(x)+1]u²-c(x)uv... under natural boundary conditions on δΩ, possesses an asymptotically stable positive steady-state solution... that has pattern D, that is, roughly speaking, as ε→0, u... converges to a positive function over D, while it converges to 0 over the rest of Ω; on the other hand, v... converges to 0 over D but converges to some positive function in the rest of Ω. In other words, the two competing species u... and v... become spatially segregated as ε→0, with u... concentrating on D and v... concentrating on ΩD. | Publication Type: | Journal Article | Source of Publication: | Journal of Differential Equations, 193(1), p. 147-179 | Publisher: | Academic Press | Place of Publication: | United States of America | ISSN: | 1090-2732 0022-0396 |
Fields of Research (FoR) 2008: | 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems | 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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