JournalsaihpcVol. 21, No. 2pp. 237–253

A minimization problem associated with elliptic systems of FitzHugh–Nagumo type

  • E.N. Dancer

    School of Mathematics and Statistics, University of Sydney, New South Wales, Sydney, 2006, Australia

  • Shusen Yan

    School of Mathematics and Statistics, University of Sydney, New South Wales, Sydney, 2006, Australia
A minimization problem associated with elliptic systems of FitzHugh–Nagumo type cover
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Abstract

We consider a minimization problem associated with the elliptic systems of FitzHugh–Nagumo type and prove that the minimizer of this minimization problem has not only a boundary layer, but also may oscillate in a set of positive measure.

Résumé

Nous étudions des solutions d’énergie minimale pour l’équation de FitzHugh–Nagumo. Nous prouvons que ces solutions ont plusieurs transitions rapids si la diffusion est petite.

Cite this article

E.N. Dancer, Shusen Yan, A minimization problem associated with elliptic systems of FitzHugh–Nagumo type. Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (2004), no. 2, pp. 237–253

DOI 10.1016/J.ANIHPC.2003.02.001