Long-time behavior for competition-diffusion systems via viscosity comparison

Lia Bronsard; Seong-A Shim

doi:10.3934/dcds.2005.13.561

Article Contents

2005, Volume 13, Issue 3: 561-581. Doi: 10.3934/dcds.2005.13.561

This issue Previous Article Lower bounds for the topological entropy Next Article Asymptotic stability of solitary waves for the Benjamin-Bona-Mahony equation

Long-time behavior for competition-diffusion systems via viscosity comparison

Lia Bronsard^1, and
Seong-A Shim^2,

1.
Department of Mathematics & Statistics, McMaster University, Hamilton, ON, L8S 4K1
2.
Department of Mathematics, Sungshin Women's University, Seoul, 136-742

Received: July 31, 2004

Revised: December 31, 2004

Published: March 2005

Abstract Related Papers Cited by

Abstract

We study the singular limit of competition-diffusion systems in population dynamics when the initial distribution of the solution is not entirely in a domain of attraction for the system. We prove comparison principles in the viscosity sense for the solution and supersolutions to the system. By using travelling wave solutions and the distance function to interfaces, we construct a viscosity supersolution. Finally we study the dynamics of interfaces and the long time behavior of the solution for the systems with large reaction rates.

Keywords:

Mathematics Subject Classification: 35K57, 53C44.

Citation:

Article Metrics

HTML views() PDF downloads(108) Cited by(0)

Long-time behavior for competition-diffusion systems via viscosity comparison

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Long-time behavior for competition-diffusion systems via viscosity comparison

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content