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
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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 . We will give a sufficient condition of for which point-condensation phenomena emerge. More precisely, for fixed , we will show that the Gierer–Meinhardt system admits a peak solution when is sufficiently small under the assumption: depends on , 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