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 ∫Ωλeujavax.xml.bind.JAXBElement@7ff7a637∼|logλ|.
Large mass boundary condensation patterns in the stationary Keller–Segel system
Vaira G.
2016-01-01
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 ∫Ωλeujavax.xml.bind.JAXBElement@7ff7a637∼|logλ|.File in questo prodotto:
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