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The aim of this paper is to study the existence of various types of peak solutions for an elliptic system of FitzHugh-Nagumo type. We prove that the system has a single peak solution, which concentrates near the boundary of the domain. Under some extra assumptions, we also construct multi-peak solutions with all the peaks near the boundary, and a single peak solution with its peak near an interior point of the domain.
@article{ASNSP_2003_5_2_4_679_0,
author = {Dancer, Edward Norman and Yan, Shusen},
title = {Peak solutions for an elliptic system of {FitzHugh-Nagumo} type},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {679--709},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 2},
number = {4},
year = {2003},
mrnumber = {2040640},
zbl = {1115.35039},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_4_679_0/}
}
TY - JOUR AU - Dancer, Edward Norman AU - Yan, Shusen TI - Peak solutions for an elliptic system of FitzHugh-Nagumo type JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2003 SP - 679 EP - 709 VL - 2 IS - 4 PB - Scuola normale superiore UR - http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_4_679_0/ LA - en ID - ASNSP_2003_5_2_4_679_0 ER -
%0 Journal Article %A Dancer, Edward Norman %A Yan, Shusen %T Peak solutions for an elliptic system of FitzHugh-Nagumo type %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2003 %P 679-709 %V 2 %N 4 %I Scuola normale superiore %U http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_4_679_0/ %G en %F ASNSP_2003_5_2_4_679_0
Dancer, Edward Norman; Yan, Shusen. Peak solutions for an elliptic system of FitzHugh-Nagumo type. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 4, pp. 679-709. http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_4_679_0/