Please use this identifier to cite or link to this item:
|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:||New York, United States||ISSN:||0022-0396||Field of Research (FOR):||010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems||Socio-Economic Outcome Codes:||970101 Expanding Knowledge in the Mathematical Sciences||Peer Reviewed:||Yes||HERDC Category Description:||C1 Refereed Article in a Scholarly Journal||Statistics to Oct 2018:||Visitors: 96
|Appears in Collections:||Journal Article|
School of Science and Technology
Files in This Item:
checked on Nov 30, 2018
checked on Mar 4, 2019
Items in Research UNE are protected by copyright, with all rights reserved, unless otherwise indicated.