A TWO-DIMENSIONAL GLIMM TYPE SCHEME ON CAUCHY PROBLEM OF TWO-DIMENSIONAL SCALAR CONSERVATION LAW

doi:10.1016/S0252-9602(16)30111-4

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (1): 1-25.doi: 10.1016/S0252-9602(16)30111-4

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A TWO-DIMENSIONAL GLIMM TYPE SCHEME ON CAUCHY PROBLEM OF TWO-DIMENSIONAL SCALAR CONSERVATION LAW

阚辉, 杨小舟

Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China

收稿日期:2016-04-05 出版日期:2017-02-25 发布日期:2017-02-25
作者简介:Hui KAN,E-mail:kanhui11@mails.ucas.ac.cn;Xiaozhou YANG,E-mail:xzyang@wipm.ac.cn

A TWO-DIMENSIONAL GLIMM TYPE SCHEME ON CAUCHY PROBLEM OF TWO-DIMENSIONAL SCALAR CONSERVATION LAW

Hui KAN, Xiaozhou YANG

Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China

Received:2016-04-05 Online:2017-02-25 Published:2017-02-25
About author:Hui KAN,E-mail:kanhui11@mails.ucas.ac.cn;Xiaozhou YANG,E-mail:xzyang@wipm.ac.cn

摘要/Abstract

摘要：

In this paper, we construct a new two-dimensional convergent scheme to solve Cauchy problem of following two-dimensional scalar conservation law
∂_tu+∂_xf(u)+∂_yg(u)=0,
u(x, y, 0)=u₀(x, y).
In which initial data can be unbounded. Although the existence and uniqueness of the weak entropy solution are obtained, little is known about how to investigate two-dimensional or higher dimensional conservation law by the schemes based on wave interaction of 2D Riemann solutions and their estimation. So we construct such scheme in our paper and get some new results.

关键词: two-dimensional conversation law, two-dimensional Glimm type scheme, Cauchy problem

Abstract:

Key words: two-dimensional conversation law, two-dimensional Glimm type scheme, Cauchy problem

阚辉, 杨小舟. A TWO-DIMENSIONAL GLIMM TYPE SCHEME ON CAUCHY PROBLEM OF TWO-DIMENSIONAL SCALAR CONSERVATION LAW[J]. 数学物理学报(英文版), 2017, 37(1): 1-25.

Hui KAN, Xiaozhou YANG. A TWO-DIMENSIONAL GLIMM TYPE SCHEME ON CAUCHY PROBLEM OF TWO-DIMENSIONAL SCALAR CONSERVATION LAW[J]. Acta mathematica scientia,Series B, 2017, 37(1): 1-25.

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A TWO-DIMENSIONAL GLIMM TYPE SCHEME ON CAUCHY PROBLEM OF TWO-DIMENSIONAL SCALAR CONSERVATION LAW

A TWO-DIMENSIONAL GLIMM TYPE SCHEME ON CAUCHY PROBLEM OF TWO-DIMENSIONAL SCALAR CONSERVATION LAW

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