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Multipeak Solutions for the Neumann Problem of an Elliptic System of Fitzhugh–Nagumo Type
Author(s) -
Dancer E. N.,
Yan Shusen
Publication year - 2005
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611504014947
Subject(s) - mathematics , bounded function , mathematics subject classification , neumann boundary condition , scalar (mathematics) , type (biology) , elliptic curve , mathematical analysis , boundary (topology) , construct (python library) , pure mathematics , geometry , computer science , ecology , biology , programming language
For systems of elliptic equations of Fitzhugh–Nagumo type on bounded domains and with small diffusion in one equation, we construct solutions with multiple sharp peaks close to each other and close to, but not on, the boundary. This is a striking contrast to results for scalar equations. For some symmetric domains, we also construct similar multipeak solutions except that here the peaks are not close to each other. 2000 Mathematics Subject Classification 35J50 (primary), 93C15 (secondary).