We consider the boundary-value problem −Δu + u = λeu in Br0 , ∂νu = 0 on ∂Br0 , where Br0 is the ball of radius r0 in RN, N 2, λ > 0 and ν is the outer normal derivative at ∂Br0 . This problem is equivalent to the stationary Keller–Segel system from chemotaxis. We show the existence of a solution concentrating at the boundary of the ball as λ goes to 0.

Steady states with unbounded mass of the Keller-Segel system / Pistoia, Angela; Vaira, Giusi. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - STAMPA. - 1:145(2015), pp. 203-222. [10.1017/S0308210513000619]

Steady states with unbounded mass of the Keller-Segel system

PISTOIA, Angela;
2015

Abstract

We consider the boundary-value problem −Δu + u = λeu in Br0 , ∂νu = 0 on ∂Br0 , where Br0 is the ball of radius r0 in RN, N 2, λ > 0 and ν is the outer normal derivative at ∂Br0 . This problem is equivalent to the stationary Keller–Segel system from chemotaxis. We show the existence of a solution concentrating at the boundary of the ball as λ goes to 0.
2015
Keller-Segl system, concentration phenomena, boundary layer
01 Pubblicazione su rivista::01a Articolo in rivista
Steady states with unbounded mass of the Keller-Segel system / Pistoia, Angela; Vaira, Giusi. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - STAMPA. - 1:145(2015), pp. 203-222. [10.1017/S0308210513000619]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/781643
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