THE GIERER & MEINHARDT SYSTEM: THE BREAKING OF HOMOCLINICS AND MULTI-BUMP GROUND STATES-Reference-Cited by-同舟云学术

THE GIERER & MEINHARDT SYSTEM: THE BREAKING OF HOMOCLINICS AND MULTI-BUMP GROUND STATES

Published:2001-08 Issue:03 Volume:03 Page:419-439
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

del PINO MANUEL¹,KOWALCZYK MICHAŁ²,CHEN XINFU³

Affiliation:

1. Departamento de Ingeniería Matemática and C.M.M., Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile

2. Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA

3. Department of Mathematics & Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA

Abstract

In this paper we study ground-states of the Gierer & Meinhardt system on the line, namely solutions of the problem [Formula: see text] We prove that given any number N, there exists a solution to this problem exhibiting exactly Nbumps in its u-component, separated from each other at a distance O(| log σ|), whenever σ is sufficiently small. These bumps resemble the shape of the unique solution of [Formula: see text]

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199701000433

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