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2003, 2003(Special): 916-925. doi: 10.3934/proc.2003.2003.916

Boundary conditions for multi-dimensional hyperbolic relaxation problems

Wen-Qing Xu 1,

1. 

Department of Mathematics, California State University, Long Beach, CA 90840

Received  September 2002 Revised  March 2003 Published  April 2003

We study the IBVP for a class of linear relaxation systems in a half space with arbitrary space dimensions. The goal is to determine the appropriate structural stability conditions, particularly, the formulation of boundary conditions such that the relaxation IBVP is stiffly well-posed or uniformly well-posed independent of the relaxation parameter. Our main contribution is the derivation, in an explicit and easily checkable form, of a stiff version of the classical Uniform Kreiss Condition (and hence referred to as Stiff Kreiss Condition). The Stiff Kreiss Condition is shown to be necessary and su±cient for the stiff well-posedness of the relaxation IBVP and its asymptotic convergence to the underlying equilibrium system in the zero relaxation limit.
Keywords: stiff Kreiss condition, conservation laws, uniform Kreiss condition, subcharacteristic condition, zero relaxation limit, boundary layers..
Mathematics Subject Classification: Primary: 35L50; Secondary: 35B25, 35B35, 35L6.
Citation: Wen-Qing Xu. Boundary conditions for multi-dimensional hyperbolic relaxation problems. Conference Publications, 2003, 2003 (Special) : 916-925. doi: 10.3934/proc.2003.2003.916
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