Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 262, Issue 11, Pages 5363-5408Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2017.02.006
Keywords
Gierer-Meinhardt system; Interior and boundary spikes; Reflection operator
Categories
Funding
- National Science Foundation [DMS-1311856]
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We prove the existence of assemblies of interior and boundary spikes as stationary solutions of the two-dimensional Gierer Meinhardt system. Moreover, we also discover that the locations of the spikes are determined by the curvature of the domain boundary together with the Green's function of the domain. A reflection operator of A is introduced to study the behaviour of the regular part of Green's function around the boundary. This reflection generalizes the well-known notions of mirror image and circle inversion for domains with sufficiently smooth boundary. (C) 2017 Elsevier Inc. All rights reserved.
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