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

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

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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: March 31, 2003

Revised: December 31, 2003

Published: May 2004

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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.

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Mathematics Subject Classification: 35K50, 35L50.

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