Perturbative techniques for the construction of spike-layers

Andrea Malchiodi

Type: Article

Publication Date: 2019-10-28

Citations: 0

DOI: https://doi.org/10.3934/dcds.2020055

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 motivated 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.

Locations

Discrete and Continuous Dynamical Systems - View - PDF

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