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边值逆问题与奇异积分方程组

本文给出了一类Ｒｉｅｍａｎｎ边值逆问题的提法及其正则型情况的解法,并利用该Ｒｉｅｍａｎｎ边值逆问题,给出了一类奇异积分方程组的新解法     

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.     

弹性力学平面问题的精确元法

本文在阶梯折算法[1]和精确解析法[2]的基础上,提出构造有限元的新方法——精确元法.该方法不用一般变分原理,可适用于任意变系数正定和非正定偏微分方程.利用该方法得到弹性力学平面问题的一个非协调任意四边形单元.它具有八个自由度.由于没有采用雅可比变换,该单元可以蜕化为三角形单元,在工程中使用起来较为方便.文中给出收敛性证明.文末给出算例,位移和应力均给出较好的结果,在单元的节点上有较好的数值精度.     

微伸缩的热弹性力学方程组柯西问题解的奇性传播

用频率分析对角化的方法,研究了一维线性微伸缩的热弹性力学方程组柯西问题解的奇性传播规律.首先从微局部观点出发,利用拟微分算子将双曲抛物的耦合方程组弱解耦.然后利用经典的双曲抛物方程理论和穿梭法,证明了柯西问题解的奇性传播具有有限传播速度、解的奇性沿双曲算子的零次特征带进行传播.     

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.     

非齐次弹性力学方程组近似解的收敛性

本文考虑满足一定条件的非齐次项的弹性力学方程组。应用补偿紧致理论,我们证明了:广义Lax-Friedrichs差分格式、Godunov差分格式或粘性方法所构造的近似解存在一个几乎处处收敛到所考虑方程组的整体弱解的子叙列。     

关于δ初值的Chaplygin压交通流AR模型的Riemann问题

研究Chaplygin压交通流AR模型初值含Dirac δ函数的Riemann问题.在广义Rankine-Hugoniot条件和熵条件下,构造性地获得了包含δ激波的整体广义解,明确地显示出四种不同的结构.结果表明,在Riemann初值这里构造的扰动下,Riemann解是稳定的.     

非线性弹性体的弹性动力学变分原理

本文根据文献[1],对非线性应力应变关系的弹性体,导出了弹性动力学问题的变分原理和广义变分原理,提出了混合位移协调元和混合应力协调元的瞬时广义变分原理.     

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.     

二维零压气体动力学系统的黎曼问题-3J情形

研究二维零压气体动力学系统带有三片常数的黎曼问题.对外波为3J的情形,借助特征分析方法,通过研究基本波的相互作用,构造了两种不同的显式解结构,一种出现了δ-激波,另一种则包含一个三角形真空区域.     

One-Dimensional Riemann Problem for Equations of Constant Pressure Fluid Dynamics with Measure Solutions by the Viscosity Method

The Riemann problem for the equations of constant pressure fluid dynamics was considered. Solutions of this problem were constructed by employing the viscosity vanishing approach. For some initial data, solutions can be viewed as bounded functions in L(R × R+) plus bounded linear functionals on C0(R× R+) with nonclassical waves as their supports. Vacuum regions appear so that uniqueness of Riemann solutions fails for some initial data.     

Riemann Problem for a Combustion Model System: the Z-N-D Solutions

The Riemann problem for a combustion model system with special kind of viscosity and chemical reaction is considered and the existence of the Riemann problem is proved. The limit of the Riemann solution as vanished viscosity is also investigated.     

Global Perturbation of the Riemann Problem for the System of Compressible Flow Through Porous Media

In this paper we consider the unperturbatcd and perturbated Riemann problem for the damped quasiliuear hyperbolic system {v_t - u_x = 0 u_t + p(v)_x = -αu, α > 0, p'(v} < 0 with initial structure of two rarefaction waves or one rarefaction wave plus one shock wave. Under certain restrictions, it admits a unique global discontinuous solution in a class of piecewise continuous and piecewise smooth functions and keeps the initial structure. Moreover, the shock strength is found decaying exponentially due to damping for the later case.     

The Riemann Hilbert Problem for General Elliptic Complex Equations of Fourth Order

§１．　ＣｏｎｄｉｔｉｏｎｓｆｏｒＧｅｎｅｒａｌＥｌｌｉｐｔｉｃＣｏｍｐｌｅｘＥｑｕａｔｉｏｎｓｏｆＦｏｕｒｔｈＯｒｄｅｒ　　ＬｅｔＤｂｅａｂｏｕｎｄｅｄｄｏｍａｉｎ,ｗｅｃｏｎｓｉｄｅｒｔｈｅｇｅｎｅｒａｌｅｌｌｉｐｔｉｃｃｏｍｐｌｅｘｅｑｕａｔｉｏｎｏｆｆｏｕｒｔｈｏｒｄｅｒｉｎｔｈｅｆｏｌｌｏｗｉｎｇｆｏｒｍｗｚ２ｚ２＝Ｆ（ｚ,ｗ,ｗｚ,ｗｚ,…,ｗｚ３,ｗｚ４,ｗｚ３ｚ,ｗｚ３ｚ,ｗｚ４）＋Ｇ（ｚ,ｗ,ｗｚ,ｗｚ,…,ｗｚ３）,Ｆ＝∑ｊ＋ｋ＝４（ｊ,ｋ）≠（２,２）Ｑｊ…     

The Riemann Problem and Matrix-Valued Potentials with a Convergent Baker-Akhiezer Function

We obtain a simple sufficient condition for the solvability of the Riemann factorization problem for matrix-valued functions on a circle. This condition is based on the symmetry principle. As an application, we consider nonlinear evolution equations that can be obtained by a unitary reduction from the zero-curvature equations connecting a linear function of the spectral parameter z and a polynomial of z. We consider solutions obtained by dressing the zero solution with a function holomorphic at infinity. We show that all such solutions are meromorphic functions on ℂ _xt ² without singularities on ℝ _xt ² . This class of solutions contains all generic finite-gap solutions and many rapidly decreasing solutions but is not exhausted by them. Any solution of this class, regarded as a function of x for almost every fixed t ∈ ℂ, is a potential with a convergent Baker-Akhiezer function for the corresponding matrix-valued differential operator of the first order.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 3, pp. 453–471, September, 2005.     

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问题的间断有限元

用时空全离散间断零次有限元对Riemarm问题进行了数值求解，没有出现振荡，很好的模拟了稀疏波的逐渐稀疏化和激波的剧烈变化。