Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773495 | Annales de l'Institut Henri Poincare (C) Non Linear Analysis | 2017 | 35 Pages |
Abstract
We consider a family of positive solutions to the system of k componentsâÎui,β=f(x,ui,β)âβui,βâjâ iaijuj,β2in Ω, where ΩâRN with Nâ¥2. It is known that uniform bounds in Lâ of {uβ} imply convergence of the densities to a segregated configuration, as the competition parameter β diverges to +â. In this paper we establish sharp quantitative point-wise estimates for the densities around the interface between different components, and we characterize the asymptotic profile of uβ in terms of entire solutions to the limit systemÎUi=Uiâjâ iaijUj2. Moreover, we develop a uniform-in-β regularity theory for the interfaces.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Nicola Soave, Alessandro Zilio,