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UID:7881@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20160301T110000
DTEND;TZID=Europe/Paris:20160301T120000
DTSTAMP:20241120T205558Z
URL:https://www.i2m.univ-amu.fr/evenements/modelling-phase-separation-with
 -coupled-elliptic-equations-recent-results-on-the-asymptotic-analysis/
SUMMARY: (...): Modelling phase separation with coupled elliptic equations:
  recent results on the asymptotic analysis
DESCRIPTION:: We consider a family of positive solutions to the system of k
  components $-\\Delta u_{i\,\\beta}=f(x\,u_{i\,\\beta})-\\beta u_{i\,\\bet
 a}\\sum_{j\neq i}a_{i\,j}u_{j\,\\beta}^2$ in $\\Omega \\subset R^N$ with $
 N\\geq 2$. It is known that uniform bounds in $L^{\\infty}$ of $\\lbrace u
 _{\\beta}\\rbrace$ imply convergence of the densities to a segregated conf
 iguration\, as the competition parameter $\\beta$ diverges to $+\\infty$. 
 In this talk I will discuss how to obtain sharp quantitative point-wise es
 timates for the densities around the interface between different component
 s\, and\, more specifically\, how to characterize the asymptotic profile o
 f $u_{\\beta}$ in terms of entire solutions to the limit system $-\\Delta 
 U_i = U_i\\sum_{j\neq i}a_{ij}U_j^2$. These results are part of an ongoing
  project with Nicola Soave.
CATEGORIES:Séminaire,Analyse Appliquée
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