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

doi:10.1016/S0252-9602(09)60012-6

数学物理学报(英文版)

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

刘红霞；潘涛

Department of Mathematics, Jinan University, Guangzhou 510632, China

收稿日期:2006-11-08 修回日期:1900-01-01 出版日期:2009-02-20 发布日期:2009-02-20
通讯作者: 刘红霞
基金资助:
The research of the first author was supported by the NSF China #10571075
and NSF-Guangdong China #04010473. The research of the second author was supported by Jinan University Foundation #51204033 and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State education Ministry #2005-383

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

Liu Hongxia; Pan Tao

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

摘要/Abstract

摘要：

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.

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

Abstract:

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

中图分类号:

35L65

刘红霞;潘涛. POINTWISE CONVERGENCE RATE OF VANISHING VISCOSITY APPROXIMATIONS FOR SCALAR CONSERVATION LAWS WITH BOUNDARY[J]. 数学物理学报(英文版), 2009, 29(1): 111-128.

Liu Hongxia; Pan Tao. POINTWISE CONVERGENCE RATE OF VANISHING VISCOSITY APPROXIMATIONS FOR SCALAR CONSERVATION LAWS WITH BOUNDARY[J]. Acta mathematica scientia,Series B, 2009, 29(1): 111-128.

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

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

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