具有时间渐退化阻尼的$2\ × 2$双曲系统的Riemann问题

IF 1 4区数学 Q1 MATHEMATICS

Boundary Value Problems Pub Date : 2023-11-14 DOI:10.1186/s13661-023-01798-z

Shiwei Li

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引用次数: 0

摘要

摘要本文研究了具有时间渐降阻尼的$2\ × 2$ 2 × 2双曲守恒律系统的Riemann问题。利用变量代换法得到了两类涉及delta冲击和真空的非自相似解。阐明了delta激波的广义Rankine-Hugoniot关系和熵条件。进一步，用消失黏度法证明了非自相似解的存在性、唯一性和稳定性。

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Riemann problem for a $2\times 2$ hyperbolic system with time-gradually-degenerate damping

Abstract This paper is focused on the Riemann problem for a $2\times 2$ 2 × 2 hyperbolic system of conservation laws with a time-gradually-degenerate damping. Two kinds of non-self-similar solutions involving the delta-shocks and vacuum are obtained using the variable substitution method. The generalized Rankine-Hugoniot relation and entropy condition are clarified for the delta-shock. Furthermore, the vanishing viscosity method proves the existence, uniqueness, and stability of non-self-similar solutions.

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来源期刊

Boundary Value Problems 数学-数学

自引率

5.90%

发文量

审稿时长

3 months

期刊介绍： The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.