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On the interior spike layer solutions to a singularly perturbed Neumann problem. (English) Zbl 0918.35024
Author’s summary: We construct interior spike layer solutions for a class of semilinear elliptic Neumann problems which arise as stationary solutions of Keller-Segel model in chemotaxis and also as limiting equations for the Gierer-Meinhardt system in biological pattern formation. We also classify the location of single interior peaks. We show exactly how the geometry of the domain affects the spike solution.
Reviewer: I.Ginchev (Varna)

MSC:
35B40Asymptotic behavior of solutions of PDE
35J65Nonlinear boundary value problems for linear elliptic equations
35B45A priori estimates for solutions of PDE
35J40Higher order elliptic equations, boundary value problems
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References:
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