一类双曲守恒律方程组的二维Riemann问题

本文中，我们构造了一类非线性双曲守恒律的二维Ｒｉｅｍａｎｎ问题的整体解。     

用L^2能量法研究粘性守恒律解的渐近性态

本文讨论单个粘性守恒律方程与具有粘性的p方程组的Cauchy问题。根据初始材料的不同情形,其相应的Reimann问题以疏散波,激波或它们的迭加为弱解。本文的目的是指出Cauchy问题的解将分别趋于疏散波,激波或它们的迭加。本文基本方法是能量积分法。文中综述了现有的成果,也提出了一些未解决的问题。     

二维双曲守恒律的大时间步长Godunov方法(英文)

考虑了关于二维守恒律的大时间步长Godunov方法.该方法是关于一维问题的自然推广.证明了文中给出的数值流函数下,该方法是守恒的.进一步还给出了近似Riemann解应满足的条件,并且证明了利用满足这些条件的近似Riemann解的大时间步长Godunov方法守恒.最后,补充证明了满足这些条件的近似Riemann解是满足熵条件的.     

非线性退化波方程的Riemann问题

研究了弹性力学中一退化波方程的Riemann问题．其应力函数非凸非凹,从而使得激波条件退化．通过引入广义激波条件下的退化激波,构造性地得到了各种情形下Riemann问题的整体解．     

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.     

间断流函数守恒律方程的高精度有限差分格式

本文研究了具有间断流函数的守恒律方程,借助本质无振荡（ENO）的思想,利用Rankine—Hugoniot关系和全局熵条件设计出一种高精度计算格式;并利用此格式计算出相关情形的Riemann问题,显示了满意的数值解果．     

非线性变换和守恒律方程的非自相似解

该文提出了一种非线性变换把一类n维单守恒律方程和初值同时降维为一维, 得到非自相似形式的全局解和基本波的表达式，并发现了非自相似解和相似解之间的本质性差别和联系     

具有泛函解的二维非线性双曲型守恒律组

本文考虑初值是分片常数且间断线经过原点的一类二维非线性双曲型守恒律组．解包含一类新的波──称之为Dirac-接触波．本文给出了这种Dirac-接触波的熵条件,方程组的解可以视为上有界线性泛函.     

广义Heisenberg方程的无穷守恒律

本文给出了Heisenberg方程的无穷守恒律,并具体给出了其前三个守恒律,特别得到了铁磁链方程无穷多个微分形式与积分形式的守恒律。     

一类微分差分方程的无穷守恒律及Backlund变换

In this paper, with the help of the Lax representation, we show the existence of infinitely many conservation laws for a differential-difference equation,which is one of the Ladic-Ablowitz hierarchy, and the conservation density and the associated flux are given for- mularlly. We also demonstrate the relation between a continuous partial differential equation and the differential-difference equation, and give Backlund transformation for the former.     

Rarefaction and Shorck Waves for Multi-Dimensional Hyperbolic Conservation Laws

This paper studies the combination of rarefaction wave and shock wave for the hyperbolic conservation laws and establishes the local existence of such combination of waves in the multi-dimensional space.     

Riemann problems for generalized gas dynamics

In this paper, a few classes of exact solutions are obtained using the differential constraints method for generalized gas dynamics equations. The solutions to Riemann problems for two different kinds of initial data are determined with a complete characterization of the solutions through shock waves and/or rarefaction waves.     

Inviscid Limit for Scalar Viscous Conservation Laws in Presence of Strong Shocks and Boundary Layers

In this paper, we study the inviscid limit problem for the scalar viscous conservation laws on half plane. We prove that if the solution of the corresponding inviscid equation on half plane is piecewise smooth with a single shock satisfying the entropy condition, then there exist solutions to the viscous conservation laws which converge to the inviscid solution away fromthe shock discontinuity and the boundary at a rate of ε^1 as the viscosity ε tends to zero.     

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.     

Some Perturbation Problems on 2x2 Nonlinear Hyperbolic Conservation Laws

We study in this paper the perturbation of elementary waves with interactions: overtaking of shock waves belonging to the same characteristic family and penetrating of a shock wave and a rarefaction wave belonging to the different characteristic family for 2 × 2 genuinely nonlinear strictly hyperbolic conservation laws. The entropy solutions for the perturbed problems are obtained by the Glimm's scheme.     

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.     

Riemann solutions without an intermediate constant state for a system of two conservation laws

We present a class of systems consisting of two conservation laws in one spatial dimension that share an intriguing property: they admit structurally stable Riemann solutions without the standard constant state. This striking phenomenon emerges in sharp contrast to what is known for strictly hyperbolic systems of conservation laws, in which the existence of constant states is necessary for the structural stability of Riemann solutions. We prove that, together, coincidence of characteristic speeds and a certain amount of genuine nonlinearity are sufficient to trigger the aforementioned phenomenon. The proof revolves about the presence of a singular point in the coincidence set that organizes the construction of our Riemann solutions.     

一类拟线性双曲组Riemann问题解的不唯一性

本文考虑一类特殊的２×２拟线性守恒律双曲组的二维Ｒｉｅｍａｎｎ问题解的不唯一性，给出解具不唯一性的例子．