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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)

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
Full Text: DOI
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