Toda system and interior clustering line concentration  for a singularly perturbed Neumann problem in two dimensional domain

Juncheng Wei; Jun Yang

doi:10.3934/dcds.2008.22.465

Article Contents

2008, Volume 22, Issue 3: 465-508. Doi: 10.3934/dcds.2008.22.465

This issue Previous Article Long-term dynamics of semilinear wave equation with nonlinear localized interior damping and a source term of critical exponent Next Article Growth rates and nonuniform hyperbolicity

Toda system and interior clustering line concentration for a singularly perturbed Neumann problem in two dimensional domain

Juncheng Wei^1, and
Jun Yang^2,

1.
Department of Mathematics, Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
2.
Department of Mathematics, Shenzhen University, Shenzhen

Received: July 2007

Revised: March 2008

Published: September 2008

Abstract Related Papers Cited by

Abstract

We consider the equation $\varepsilon^2\Delta$ ũ-ũ+ũ$^p =0$ in a bounded, smooth domain $\Omega$ in $\R^2$ under homogeneous Neumann boundary conditions. Let $\Gamma$ be a segment contained in $\Omega$, connecting orthogonally the boundary, non-degenerate and non-minimal with respect to the curve length. For any given integer $N\ge 2$ and for small $\varepsilon$ away from certain critical numbers, we construct a solution exhibiting $N$ interior layers at mutual distances $O(\varepsilon|\ln\varepsilon|)$ whose center of mass collapse onto $\Gamma$ at speed $O(\varepsilon^{1+\mu})$ for small positive constant $\mu$ as $\varepsilon\to 0$. Asymptotic location of these layers is governed by a Toda system.

Keywords:

Mathematics Subject Classification: Primary: 35B25, 35J60; Secondary: 35K99, 92C40.

Citation:

Article Metrics

HTML views() PDF downloads(95) Cited by(0)

Toda system and interior clustering line concentration for a singularly perturbed Neumann problem in two dimensional domain

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Toda system and interior clustering line concentration for a singularly perturbed Neumann problem in two dimensional domain

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content