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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:

35B40 Asymptotic behavior of solutions to PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
35B45 A priori estimates in context of PDEs
35J40 Boundary value problems for higher-order elliptic equations
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