THE SHOCK CURVE APPROACH TO THE RIEMANN PROBLEM FOR 2 × 2 HYPERBOLIC SYSTEMS OF CONSERVATION LAWS
THE SHOCK CURVE APPROACH TO THE RIEMANN PROBLEM FOR 2 × 2 HYPERBOLIC SYSTEMS OF CONSERVATION LAWS
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2×2双曲守恒定律系黎曼问题的激波曲线法
DOI：
10.1142/s0219891610002128
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发表时间：
2010
影响因子：
0.7
通讯作者：
Hiroki Ohwa
中科院分区：
文献类型：
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作者：
Hiroki Ohwa
本文考虑单空间变量2 × 2双曲型守恒律组的Riemann问题.我们的主要假设是通量的弗雷歇导数（雅可比矩阵）内的非对角元素的乘积是正的，并且系统是真正的非线性。第一个假设意味着系统是严格双曲的，但我们不需要像Smoller-Johnson条件那样的凸性条件。通过使用激波曲线的方法，我们表明，这两个假设是足够的，以建立满足Lax熵条件的自相似解决方案的唯一性在不连续。
We consider the Riemann problem for 2 × 2 hyperbolic systems of conservation laws in one space variable. Our main assumptions are that the product of non-diagonal elements within the Frechet derivative (Jacobian) of the flux is positive, and that the system is genuinely nonlinear. The first assumption implies that the system is strictly hyperbolic, but we do not require a convexity-like condition such as the Smoller–Johnson condition. By using the shock curve approach, we show that those two assumptions are sufficient to establish the uniqueness of self-similar solutions satisfying the Lax entropy conditions at discontinuities.
具有二次通量的双曲守恒律 2x2 系统中 Hugoniot 曲线的几何
DOI：
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发表时间：
2005
期刊：
IMA Journal of Applied Mathematics 70
影响因子：
--
作者：
Fumioki Asakura;Mitsuru Yamazaki
通讯作者：
Mitsuru Yamazaki