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Steady states with unbounded mass of the Keller–Segel system

Published online by Cambridge University Press:  30 January 2015

Angela Pistoia  and
Giusi Vaira
Angela Pistoia
Affiliation:
Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Universitá La Sapienza, Via A. Scarpa 14, 00185 Roma, Italy, (angela.pistoia@sbai.uniroma1.it; giusi.vaira@sbai.uniroma1.it)
Giusi Vaira
Affiliation:
Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Universitá La Sapienza, Via A. Scarpa 14, 00185 Roma, Italy, (angela.pistoia@sbai.uniroma1.it; giusi.vaira@sbai.uniroma1.it)
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Abstract

We consider the boundary-value problem

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 1 , February 2015 , pp. 203 - 222
Copyright
Copyright © Royal Society of Edinburgh 2015 

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