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

Abstract

Boundary concentration

KeyWords Plus:PERTURBED NEUMANN PROBLEM

CHEMOTAXIS

CURVES

STEADY-STATES

We consider the boundary value problem { -Delta u + u = lambda e(u), in Omega partial derivative(v)u = 0 on partial derivative Omega, where Omega is a bounded smooth domain in R-2, lambda > 0 and v is the inner normal derivative at partial derivative Omega. This problem is equivalent to the stationary Keller-Segel system from chemotaxis. We establish the existence of a solution u(lambda) which exhibits a sharp boundary layer along the entire boundary partial derivative Omega as lambda -> 0. These solutions have large mass in the sense that integral(Omega) lambda e(u lambda) similar to | log lambda|. (C) 2016 Elsevier Inc. All rights reserved. Keywords: Author Keywords:Keller-Segel system