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

Huey-Er Lin Institute of Mathematics, Academia Sinica Jian-Guo Liu University of Maryland Wen-Qing Xu California State University

Analysis of PDEs mathscidoc:1702.03066

Communications on Pure and Applied Analysis , 3, (2), 267 - 290, 2004.6
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.
Convection-diffusion equations, hyperbolic equations, zero viscosity limit, far field boundary condition, boundary layer.
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@inproceedings{huey-er2004effects,
  title={Effects of small viscosity and far field boundary conditions for hyperbolic systems},
  author={Huey-Er Lin, Jian-Guo Liu, and Wen-Qing Xu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209101925857384374},
  booktitle={Communications on Pure and Applied Analysis },
  volume={3},
  number={2},
  pages={267 - 290},
  year={2004},
}
Huey-Er Lin, Jian-Guo Liu, and Wen-Qing Xu. Effects of small viscosity and far field boundary conditions for hyperbolic systems. 2004. Vol. 3. In Communications on Pure and Applied Analysis . pp.267 - 290. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209101925857384374.
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