In this paper we survey some results concerning the construction of spike-layers, namely solutions to singularly perturbed equations that exhibit a concentration behaviour. Their study is moti- vated by the analysis of pattern formation in biological systems such as the Keller-Segel or the Gierer- Meinhardt’s. We describe some general perturbative variational strategy useful to study concentration at points, and also at spheres in radially symmetric situations.
Perturbative techniques for the construction of spike-layers
Andrea Malchiodi
2020
Abstract
In this paper we survey some results concerning the construction of spike-layers, namely solutions to singularly perturbed equations that exhibit a concentration behaviour. Their study is moti- vated by the analysis of pattern formation in biological systems such as the Keller-Segel or the Gierer- Meinhardt’s. We describe some general perturbative variational strategy useful to study concentration at points, and also at spheres in radially symmetric situations.File in questo prodotto:
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