Point-condensation phenomena and saturation effect for the one-dimensional Gierer–Meinhardt system

  • Kotaro Morimoto

    Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1 Minami-Ohsawa, Hachioji, Tokyo 192-0397, Japan

Abstract

In this paper, we are concerned with peak solutions to the following one-dimensional Gierer–Meinhardt system with saturation:

where , , . The saturation effect of the activator is given by the parameter κ. We will give a sufficient condition of κ for which point-condensation phenomena emerge. More precisely, for fixed , we will show that the Gierer–Meinhardt system admits a peak solution when ε is sufficiently small under the assumption: κ depends on ε, namely, , and there exists a limit for certain .

Cite this article

Kotaro Morimoto, Point-condensation phenomena and saturation effect for the one-dimensional Gierer–Meinhardt system. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 4, pp. 973–995

DOI 10.1016/J.ANIHPC.2010.01.003