Scalar Conservation Laws with Boundary Effect

Tao Pan () and Hongxia Liu ()
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Tao Pan: Guangxi University, Dept. of Mathematics and Information Sciences
Hongxia Liu: Jinan University, Dept. of Mathematics

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2003, pp 775-787 from Springer

Abstract: Abstract This paper reviews the recent work on the global weak entropy solutions of scalar conservation laws with boundary effect and the global error estimate for viscosity methods to initial-boundary value problems of scalar conservation laws. In section 2, we state how to obtain the existence of weak entropy solution for general nonconvex scalar conservation laws by Dafermos’s polygonal approximations method which can be used to simulate geometric structure of the weak entropy solution. We also state the large time behaviors of weak entropy solution by discussing the interaction of elementary waves for scalar convex conservation laws on a bounded domain. In section 3, we are concerned with the global error estimate for viscous approximations to inviscid solution to initial-boundary value problems of convex scalar conservation laws by the matching traveling wave solutions method.

Keywords: Elementary Wave; Viscosity Method; Weak Entropy Solution; Viscous Shock Wave; Global Error Estimate (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55711-8_73

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DOI: 10.1007/978-3-642-55711-8_73

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