非等熵Chaplygin气体极限黎曼解 关于扰动的依赖性

主要研究了非等熵Chaplygin气体黎曼问题初值扰动后解的结构,分析了经典的黎曼问题和扰动问题解的结构及极限结构,发现后者的极限解在δ质量权趋于零时不同于前者解的结构.该结果表明对非等熵Chaplygin气体而言,经典的黎曼问题与带δ初值的黎曼问题有着本质的区别.     

绝热流Chaplygin气体的Riemann问题

本文研究了绝热流Chaplygin气体动力学方程组,利用特征分析方法,在得到所有基本波的基础上,构造出Riemann问题的所有解.Riemann解由前向疏散波(激波)、后向疏散波(激波)、接触间断以及δ波构成.     

Stability of the Riemann solutions for a Chaplygin gas

In this paper, we study the structural stability of solutions to the Riemann problem for one-dimensional isentropic Chaplygin gas. We perturb the Riemann initial data by taking three piecewise constant states and construct the global structure. By letting the perturbed parameter ε$\epsilon$ tend to zero, we prove that the Riemann solutions are stable under the local small perturbations of the Riemann initial data even when the initial perturbed density depending on the parameter but with no mass concentration limit.     

Riemann problem for Chaplygin gas with combustion

We study the Riemann problem of the Chapman–Jouguet model for an ideal combustible Chaplygin gas. By analyzing the wave curves in the phase plane, we obtain constructively the unique solution of the Riemann problem under the global entropy conditions.     

The limits of Riemann solutions for the isentropic Euler system with extended Chaplygin gas

The Riemann problem for the isentropic Euler system with the state equation for the extended Chaplygin gas is considered, and the Riemann solutions are constructed completely for all the cases. The limiting relations of Riemann solutions for the isentropic Euler system with the state equation from the extended Chaplygin gas to the Chaplygin gas are derived in detail when the corrected term tends to zero. The formation of delta shock wave solution and two-contact-discontinuity solution is investigated during the process of taking the limit.     

Riemann problem for the relativistic Chaplygin Euler equations

The relativistic Euler equations for a Chaplygin gas are studied. The Riemann problem is solved constructively. There are five kinds of Riemann solutions, in which four only contain different contact discontinuities and the other involves delta shock waves. Under suitable generalized Rankine-Hugoniot relation and entropy condition, the existence and uniqueness of delta-shock solutions are established.     

带有源项的广义Chaplygin气体磁流体Euler方程组Riemann解的极限

研究了带有源项的广义Chaplygin气体磁流体Euler方程组Riemann解的极限.由于非齐次项的影响,带有源项的广义Chaplygin气体磁流体Euler方程组Riemann解不再是自相似的.当压力和磁感强度同时消失时,它的解会收敛到零压流输运方程组的Riemann解,解中会出现δ-激波和真空现象.同时研究还得到了仅当磁感强度消失时,它的解会收敛到非齐次广义Chaplygin气体Euler方程组的Riemann解,并且解中只出现δ-激波.     

具有负压力的Aw-Rascle交通流的Riemann问题

研究了广义Chaplygin气体的Aw-Rascle交通流的Riemann问题,构建了它的古典和非古典Riemann解.借助广义Rankine-Hugoniot关系和δ-激波熵条件,获得了δ-激波解的存在性和唯一性,并且给出一些数值模拟来阐明此分析.     

Vanishing pressure limits of Riemann solutions to the isentropic relativistic Euler system for Chaplygin gas

The Riemann solutions to the isentropic relativistic Euler system for Chaplygin gas with a small parameter are considered. Unlike the polytropic or barotropic gas cases, we find that firstly, as the parameter decreases to a certain critical number, the two-shock solution converges to a delta shock wave solution of the same system. Moreover, as the parameter goes to zero, that is, the pressure vanishes, the solution is nothing but the delta shock wave solution to the zero-pressure relativistic Euler system. Meanwhile, the two-rarefaction wave solution tends to the vacuum solution to the zero-pressure relativistic system, and the solution containing one rarefaction wave and one shock wave tends to the contact discontinuity solution to the zero-pressure relativistic system as pressure vanishes.     

广义Chaplygin气体磁流体力学方程组的Riemann问题

利用特征分析和相平面分析的方法,由Rankine-Hugoniot条件和稳定性条件,构造性地得到了一维等熵广义Chaplygin气体磁流体力学方程组的Riemann解的存在唯一性.同时,详细研究了疏散波曲线和激波曲线的性质.     

The Non-selfsimilar Riemann Problem for 2-D Zero-Pressure Flow in Gas Dynamics

The non-selfsimilar Riemann problem for two-dimensional zero-pressure flow in gas dynamics with two constant states separated by a convex curve is considered.By means of the generalized Rankine-Hugoniot relation and the generalized characteristic analysis method,the global solution involving delta shock wave and vacuum is constructed.The explicit solution for a special case is also given.     

Riemann boundary value problems and reflection of shock for the Chaplygin gas

In this paper,we study two-dimensional Riemann boundary value problems of Euler system for the isentropic and irrotational Chaplygin gas with initial data being two constant states given in two sectors respectively,where one sector is a quadrant and the other one has an acute vertex angle.We prove that the Riemann boundary value problem admits a global self-similar solution,if either the initial states are close,or the smaller sector is also near a quadrant.Our result can be applied to solving the problem of shock reflection by a ramp.     

耗散等熵气体动力学方程组广义Riemann问题

The paper concerns with generalized Riemann problem for isentropic flow with dissipation, and show that if the similarity solution to Riemann problem is composed of a backward centered rarefaction wave and a forward centered rarefaction wave, then general-ized Riemann problem admits a unique global solution on t ≥ 0. This solution is composed of backward centered wave and a forward centered wave with the origin as their center and then continuous for t>0.     

Interactions of delta shock waves for the Chaplygin gas equations with split delta functions

In this article, we study the interactions of delta shock waves for the one-dimensional Euler equations for Chaplygin gas with split delta functions. We constructively obtain the solutions when the initial data are three piecewise constant states. The global structure and large time-asymptotic behaviors of the solutions are analyzed case by case. Moreover, we obtain the stability of solutions by letting perturbed parameter ? tend to zero.     

气体动力学燃烧模型的广义Riemann问题

考察了在(x,t)平面上原点(t＞0)的邻域内气体动力学燃烧模型的广义Riemann问题．在改进的熵条件下构造了此问题的唯一解．它们是自相似ZND燃烧模型的极限．发现对某些情形,广义Riemann问题的解与相应的Riemann问题的解有本质的不同．特别地,扰动会使得相应Riemann问题的强爆轰波转化为由预压激波点燃的弱爆燃波．在一些情形,尽管相应的Riemann解中不含燃烧波,扰动后燃烧波会出现．这反映了未燃气体的不稳定性．     

Riemann problem with Delta initial data for the relativistic Chaplygin Euler equations

In this paper, we study the Riemann problem with the initial data containing the Dirac delta function for the relativistic Chaplygin Euler equations. Under the generalized Rankine-Hugoniot conditions and entropy condition, we constructively obtain the global existence of generalized solutions including delta shock waves that explicitly exhibit four kinds of different structures. Moreover, we obtain the stability of generalized solutions by making use of the perturbation of the initial data     

Gradient estimate in terms of a Hilbert-like distance,for minimal surfaces and Chaplygin gas

We consider a quasilinear elliptic boundary value-problem with homogenenous Dirichlet condition. The data are a convex planar domain. The gradient estimate is needed to ensure the uniform ellipticity, before applying regularity theory. We establish this estimate in terms of a distance, which is equivalent to the Hilbert metric.

This fills the proof of existence and uniqueness of a solution to this BVP (boundary-value problem), when the domain is only convex but not strictly, for instance if it is a polygon.     

Delta-shocks and vacuum states in the vanishing pressure limit of solutions to the isentropic Euler equations for modified Chaplygin gas

The phenomena of concentration and cavitation and the formation of δ-shocks and vacuum states in solutions to the isentropic Euler equations for a modified Chaplygin gas are analyzed as the double parameter pressure vanishes. Firstly, the Riemann problem of the isentropic Euler equations for a modified Chaplygin gas is solved analytically. Secondly, it is rigorously shown that, as the pressure vanishes, any two-shock Riemann solution to the isentropic Euler equations for a modified Chaplygin gas tends to a δ-shock solution to the transport equations, and the intermediate density between the two shocks tends to a weighted δ-measure that forms the δ-shock; any two-rarefaction-wave Riemann solution to the isentropic Euler equations for a modified Chaplygin gas tends to a two-contact-discontinuity solution to the transport equations, the nonvacuum intermediate state between the two rarefaction waves tends to a vacuum state. Finally, some numerical results exhibiting the formation of δ-shocks and vacuum states are presented as the pressure decreases.     

一维Chaplygin气体欧拉方程组中波的相互作用

研究一维Chaplygin气体欧拉方程组中波的相互作用.方程组的波包含接触间断和在密度变量以及内能变量上同时具有狄拉克函数的狄拉克激波.根据这些波的不同组合,问题被分成了7种情形.通过详细地构造每种情形的整体解,获得了各种波相互作用的完整结果.特别地,对于一类初值,两个接触间断相互作用后,产生了一个狄拉克激波;然而,对于另外一类初值,一个狄拉克激波与一个接触间断相互作用后,狄拉克激波消失.这些都是波相互作用中非常特别的现象.