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Multipeak solutions for the Neumann problem of an elliptic system of Fitzhugh–Nagumo type

Published online by Cambridge University Press:  16 December 2004

E. N. Dancer  and
Shusen Yan
E. N. Dancer
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia. E-mail: normd@maths.usyd.edu.au
Shusen Yan
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia. E-mail: shusen@maths.usyd.edu.au
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Abstract

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.

Keywords

35J50 (primary)93C15 (secondary)
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 90 , Issue 1 , January 2005 , pp. 209 - 244
Copyright
2004 London Mathematical Society

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Footnotes

This work was supported by the ARC.