THE RIEMANN PROBLEM FOR A TWO-DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS WITH NON-CLASSICAL SHOCK WAVES

数学物理学报(英文版) ›› 1998, Vol. 18 ›› Issue (1): 45-56.

THE RIEMANN PROBLEM FOR A TWO-DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS WITH NON-CLASSICAL SHOCK WAVES

胡家信

Wuhan Institute of Physics and Mathematics, Academia Sinica, Wuhan 430071, China

收稿日期:1995-11-06 修回日期:1997-01-29 出版日期:1998-03-25 发布日期:1998-03-25
基金资助:
Supported by the Young Scientist Laboratory of Mathematical Physics

THE RIEMANN PROBLEM FOR A TWO-DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS WITH NON-CLASSICAL SHOCK WAVES

Hu Jiaxin

Wuhan Institute of Physics and Mathematics, Academia Sinica, Wuhan 430071, China

Received:1995-11-06 Revised:1997-01-29 Online:1998-03-25 Published:1998-03-25
Supported by:
Supported by the Young Scientist Laboratory of Mathematical Physics

摘要/Abstract

摘要： The Riemann problem for a two-dimensional 2×2 nonstrictly hyperbolic system of nonlinear conservaion laws has been solved thoroughly for any gived initial data which are constant in each quadrant. The non-classical shock waves, which are labelled as δ-shock waves, appear in some solutions. The solutions have been obtained are hot unique. Due to the specific property of the system considered, there are no rarefaction waves in solution.This paper is divided into three parts. The first part constructs Riemann solutions for initial data involving two contact discontinuities while the second considers the case for other initial data. The last part briefly discusses the non-uniqueness of the solutions.

关键词: Riemann problem, two-dimensions hyperbolic system, non-classical wave

Abstract: The Riemann problem for a two-dimensional 2×2 nonstrictly hyperbolic system of nonlinear conservaion laws has been solved thoroughly for any gived initial data which are constant in each quadrant. The non-classical shock waves, which are labelled as δ-shock waves, appear in some solutions. The solutions have been obtained are hot unique. Due to the specific property of the system considered, there are no rarefaction waves in solution.This paper is divided into three parts. The first part constructs Riemann solutions for initial data involving two contact discontinuities while the second considers the case for other initial data. The last part briefly discusses the non-uniqueness of the solutions.

Key words: Riemann problem, two-dimensions hyperbolic system, non-classical wave

胡家信. THE RIEMANN PROBLEM FOR A TWO-DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS WITH NON-CLASSICAL SHOCK WAVES[J]. 数学物理学报(英文版), 1998, 18(1): 45-56.

Hu Jiaxin. THE RIEMANN PROBLEM FOR A TWO-DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS WITH NON-CLASSICAL SHOCK WAVES[J]. Acta mathematica scientia,Series B, 1998, 18(1): 45-56.

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THE RIEMANN PROBLEM FOR A TWO-DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS WITH NON-CLASSICAL SHOCK WAVES

THE RIEMANN PROBLEM FOR A TWO-DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS WITH NON-CLASSICAL SHOCK WAVES

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