We consider the boundary value problem −Δu+u=λeu,inΩ∂νu=0on∂Ω where Ω is a bounded smooth domain in R2, λ>0 and ν is the inner normal derivative at ∂Ω. This problem is equivalent to the stationary Keller–Segel system from chemotaxis. We establish the existence of a solution uλ which exhibits a sharp boundary layer along the entire boundary ∂Ω as λ→0. These solutions have large mass in the sense that ∫Ωλeuλ∼|log⁡λ|.

Large mass boundary condensation patterns in the stationary Keller–Segel system

VAIRA, Giusi
2016

Abstract

We consider the boundary value problem −Δu+u=λeu,inΩ∂νu=0on∂Ω where Ω is a bounded smooth domain in R2, λ>0 and ν is the inner normal derivative at ∂Ω. This problem is equivalent to the stationary Keller–Segel system from chemotaxis. We establish the existence of a solution uλ which exhibits a sharp boundary layer along the entire boundary ∂Ω as λ→0. These solutions have large mass in the sense that ∫Ωλeuλ∼|log⁡λ|.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11591/368437
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? ND
social impact