Acta mathematica scientia,Series B

• Articles • Previous Articles     Next Articles

POINTWISE CONVERGENCE RATE OF VANISHING VISCOSITY APPROXIMATIONS FOR SCALAR CONSERVATION LAWS WITH BOUNDARY

Liu Hongxia; Pan Tao   

  1. Department of Mathematics, Jinan University, Guangzhou 510632, China
  • Received:2006-11-08 Revised:1900-01-01 Online:2009-02-20 Published:2009-02-20
  • Contact: Liu Hongxia

Abstract:

This article is concerned with the pointwise error estimates for vanishing vis-
cosity approximations to scalar convex conservation laws with boundary. By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang, an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws, whose weak entropy solution is piecewise C2-smooth with interaction of elementary waves and the boundary. The analysis method in this article can be used to deal with the case in which the piecewise smooth solutions of inviscid have finitely many waves with possible all kinds of interaction with the boundary.

Key words: Scalar conservation laws with boundary, vanishing viscosity approximations,
error estimate,
pointwise convergence rate, transport inequality

CLC Number: 

  • 35L65
Trendmd