The Riemann problem for the Suliciu relaxation system with the double-coefficient Coulomb-like friction terms

Zhang Yanyan; Zhang Yu

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The Riemann problem for the Suliciu relaxation system with the double-coefficient Coulomb-like friction terms

机译：具有双系数类库仑摩擦项的苏里休弛豫系统的黎曼问题

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摘要

We solve the Riemann problem for the Suliciu relaxation system with the Coulomb-like friction terms containing two constant friction coefficients. The exact Riemann solutions involving delta shock waves and contact discontinuities are obtained constructively. Via deriving the generalized Rankine-Hugoniot relations of delta shock waves in detail, all of the position, propagation speed and strength of the delta shock wave are given concretely under a suitable entropy condition. Based on this, we clearly analyze the influence of the Coulomb-like friction terms on the Riemann solutions of the Suliciu relaxation system.

机译：我们使用包含两个恒定摩擦系数的类库仑摩擦项来解决Suliciu松弛系统的黎曼问题。构造性地获得了涉及δ冲击波和接触不连续性的精确黎曼解。通过详细推导三角波冲击波的广义兰金-休格尼奥关系，具体给出了在适当的熵条件下三角波冲击波的所有位置，传播速度和强度。在此基础上，我们清楚地分析了库仑式摩擦项对Suliciu松弛系统的Riemann解的影响。

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《International journal of non-linear mechanics》 |2019年第11期|200-210|共11页
作者
Zhang Yanyan; Zhang Yu;
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作者单位

Xinyang Normal Univ Coll Math & Stat Xinyang 464000 Peoples R China;

Yunnan Normal Univ Dept Math Kunming 650091 Yunnan Peoples R China;

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正文语种 eng
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关键词
Suliciu relaxation system; Coulomb-like friction term; Riemann problem; Delta shock wave;

机译：Suliciu放松系统;库仑式摩擦项;黎曼问题;三角洲冲击波;

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专利

1. The Riemann problem for the Suliciu relaxation system with the double-coefficient Coulomb-like friction terms [J] . Zhang Yanyan, Zhang Yu International journal of non-linear mechanics . 2019,第NOVa期

机译：具有双系数类库仑摩擦项的苏里休弛豫系统的黎曼问题
2. The Riemann problem for the pressureless Euler system with the Coulomb-like friction term [J] . Shen Chun IMA Journal of Applied Mathematics . 2016,第1期

机译：具有库仑式摩擦项的无压欧拉系统的黎曼问题
3. The Convergence of Riemann Solutions to the Modified Chaplygin Gas Equations with a Coulomb-Like Friction Term as the Pressure Vanishes [J] . Yongqiang Fan, Lihui Guo, Gan Yin Advances in Mathematical Physics . 2018,第1期

机译：压力消失时具有库仑式摩擦项的修改后的Chaplygin气体方程的Riemann解的收敛性
4. RELAXATION-BASED APPROXIMATE RIEMANN SOLVERS FOR ELASTIC RODS [C] . KNUT WAAGAN International Conference on Hyperbolic Problems . 2014

机译：基于放松的近似Riemann载体弹性杆
5. Part I. An extension of the Riemann problems and Glimm's method to general systems of conservation laws with source terms. Part II. A total variation bound on the conserved quantities for a generic resonant nonlinear balance laws. [D] . Hong, John Meng-Kai. 2000

机译：第一部分，将黎曼问题和格里姆方法扩展到带有来源条款的一般保护法体系。第二部分对于一般的共振非线性平衡定律，守恒量的总变化量是有限的。
6. A Potential Elastohydrodynamic Origin of Load-Support and Coulomb-Like Friction in Lung/Chest Wall Lubrication [O] . James P. Butler, Stephen H. Loring -1

机译：肺部/胸部壁润滑中潜在的载荷支持和库仑摩擦的弹性流体力学起源
7. Modified Suliciu relaxation system and exact resolution of isolated shock waves [O] . Chalons Christophe, Coquel Frédéric 2012

机译：改进的Suliciu松弛系统和孤立冲击波的精确分辨率
8. Internal Friction Associated with Dislocation Relaxations in Virgin Martensite [R] . Yong, L. 1993

机译：内部摩擦与维尔京马氏体中的位错松弛有关

The Riemann problem for the Suliciu relaxation system with the double-coefficient Coulomb-like friction terms

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