Generalized Glimm scheme to the initial boundary value problem of hyperbolic systems of balance laws

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/51131

Title:	Generalized Glimm scheme to the initial boundary value problem of hyperbolic systems of balance laws
Authors:	Hong,JM;Su,YC
Contributors:	數學系
Date:	2010
Issue Date:	2012-03-27 18:22:48 (UTC+8)
Publisher:	國立中央大學
Abstract:	In this paper we provide a generalized version of the Glimm scheme to establish the global existence of weak solutions to the initial-boundary value problem of 2 x 2 hyperbolic systems of conservation laws with source terms. We extend the methods in [J.B. Goodman, Initial boundary value problem for hyperbolic systems of conservation laws, Ph.D. Dissertation. Stanford University, 1982; J.M. Hong, An extension of Glimm's method to inhomogeneous strictly hyperbolic systems of conservation laws by "weaker than weak" solutions of the Riemann problem, J. Differential Equations 222 (2006) 515-549] to construct the approximate solutions of Riemann and boundary Riemann problems, which can be adopted as the building block of approximate solutions for our initial-boundary value problem. By extending the results in U. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18 (1965) 697-715] and showing the weak convergence of residuals, we obtain stability and consistency of the scheme. (C) 2009 Elsevier Ltd. All rights reserved.
Relation:	NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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