Effects of small viscosity and far field boundary conditions for hyperbolic systems

Huey-Er Lin; Jian-Guo Liu; Wen-Qing Xu

doi:10.3934/cpaa.2004.3.267

Article Contents

2004, Volume 3, Issue 2: 267-290. Doi: 10.3934/cpaa.2004.3.267

This issue Previous Article Multiple solutions with changing sign energy to a nonlinear elliptic equation Next Article On the existence of quasi periodic and almost periodic solutions of neutral functional differential equations

Effects of small viscosity and far field boundary conditions for hyperbolic systems

1.
Institute of Mathematics, Academia Sinica, Taipei 11529
2.
IPST and Department of Mathematics, University of Maryland, College Park, MD 20742
3.
Department of Mathematics, California State University, Long Beach, CA 90840

Received: April 2003

Revised: January 2004

Published: June 2004

Abstract / Introduction Related Papers Cited by

Abstract

In this paper we study the effects of small viscosity term and the far-field boundary conditions for systems of convection-diffusion equations in the zero viscosity limit. The far-field boundary conditions are classified and the corresponding solution structures are analyzed. It is confirmed that the Neumann type of far-field boundary condition is preferred. On the other hand, we also identify a class of improperly coupled boundary conditions which lead to catastrophic reflection waves dominating the inlet in the zero viscosity limit. The analysis is performed on the linearized convection-diffusion model which well describes the behavior at the far field for many physical and engineering systems such as fluid dynamical equations and electro-magnetic equations. The results obtained here should provide some theoretical guidance for designing effective far field boundary conditions.

Keywords:

Mathematics Subject Classification: 35K50, 35L50.

Citation:

Article Metrics

HTML views() PDF downloads(55) Cited by(0)

Effects of small viscosity and far field boundary conditions for hyperbolic systems

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Effects of small viscosity and far field boundary conditions for hyperbolic systems

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content