Stationary solutions to a Keller-Segel chemotaxis system

被引:0
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作者
Musso, Monica
Wei, Juncheng
机构
[1] Pontificia Univ Catolica Chile, Dept Matemat, Macul, Chile
[2] Politecn Torino, Dipartimento Matemat, I-10129 Turin, Italy
[3] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China
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中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider the following stationary Keller-Segel system from chemotaxis Delta u - au + u(p) = 0, u > 0 in Omega, partial derivative u/partial derivative v = 0 on partial derivative Omega, where Omega subset of R-2 is a smooth and bounded domain. We show that given any two positive integers K,L, for p sufficiently large, there exists a solution concentrating in K interior points and L boundary points. The location of the blow-up points is related to the Green function. The solutions are obtained as critical points of some finite-dimensional reduced energy functional. No assumption on the symmetry, geometry nor topology of the domain is needed.
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页码:217 / 247
页数:31
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