# American Institute of Mathematical Sciences

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June  2004, 3(2): 267-290. doi: 10.3934/cpaa.2004.3.267

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

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

Received  April 2003 Revised  January 2004 Published  March 2004

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.
Citation: Huey-Er Lin, Jian-Guo Liu, Wen-Qing Xu. Effects of small viscosity and far field boundary conditions for hyperbolic systems. Communications on Pure & Applied Analysis, 2004, 3 (2) : 267-290. doi: 10.3934/cpaa.2004.3.267
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