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Title: An Elliptic Problem Related to Planar Vortex Pairs
Contributor(s): Li, Gongbao (author); Yan, Shusen  (author); Yang, Jianfu (author)
Publication Date: 2005
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Abstract: In this paper, we study the existence and limiting behavior of the mountain pass solutions of the elliptic problem —Δu = λf(u — q(x)) in Ω C ℝ²; u 0 on ∂Ω, where q is a positive harmonic function. We show that the 'vortex core' Aλ = {x ∈ Ω: uλ (x) > q(x)} of the solution uλ, shrinks to a global minimum point of q on the boundary ∂Ω as λ → + ∞. Furthermore, we show that for each strict local minimum x₀ point of q(x) on the boundary ∂Ω, there exists a solution uλ whose vortex core shrinks to this strict local minimum point x₀ as λ → +∞.
Publication Type: Journal Article
Source of Publication: SIAM Journal on Mathematical Analysis, 36(5), p. 1444-1460
Publisher: Society for Industrial and Applied Mathematics
Place of Publication: Philadelphia, PA, United States
ISSN: 0036-1410
Field of Research (FOR): 019999 Mathematical Sciences not elsewhere classified
Socio-Economic Objective (SEO): 970101 Expanding Knowledge in the Mathematical Sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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