Boundary conditions for multi-dimensional hyperbolic relaxation problems

Pages: 916 - 925, Issue Special, July 2003

 Abstract        Full Text (186.1K)              

Wen-Qing Xu - Department of Mathematics, California State University, Long Beach, CA 90840, United States (email)

Abstract: 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:  conservation laws, zero relaxation limit, subcharacteristic condition, uniform Kreiss condition, stiff Kreiss condition, boundary layers.
Mathematics Subject Classification:  Primary: 35L50; Secondary: 35B25, 35B35, 35L65.

Received: September 2002;      Revised: March 2003;      Published: April 2003.