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．     

压差方程Chapman-Jouguet燃烧模型爆轰波与激波的相互作用

研究了气体动力学压差方程Chapman-Jouguet(CJ)燃烧模型爆轰波与激波的相互作用.给出了该CJ燃烧模型的几类基本波线:激波线、疏散波线、强爆轰波线和CJ爆轰波线.通过研究该CJ燃烧模型的初值为三片常状态的一类初值问题,并利用相平面分析的方法构造出该问题的整体分片光滑解,得到了压差方程CJ燃烧模型爆轰波与激波相互作用的结果.进一步地,得到了对应燃烧Riemann问题解的初值扰动稳定性.     

相变演化Suliciu模型中波的相互作用

描述相变演化的Suliciu模型，其基本波可由行波分析得到．对于任何给定分两段常值的初始状态，相应的Riemann解是某些基本波的组合．对分三段常值的初始状态，解由上述Piemann解构成，其中相邻两状态间以基本波连接．当基本波发生碰撞时，新的Riemann问题形成．通过研究这些Riemann。问题，可以在适当的参数空间中对基本波之间复杂的相互作用加以分类．     

分数阶广义扰动热波方程的与泛函映射解

研究了一类分数阶广义非线性扰动热波方程.首先在典型分数阶热波方程情形下得到解,接着用泛函分析映射方法,求出了分数阶广义非线性扰动热波方程初始边值问题的任意次近似解析解.最后简述了它的物理意义.求得的近似解析解,弥补了单纯用数值方法得到的模拟解的不足.     

一类二维单个守恒律方程的Riemann问题

本文研究一类二维单个守恒律方程的Riemann问题.用广义特征分析方法研究了这类方程,给出了基本波的分类,解决了初值为两片常数的二维Riemann问题,给出了Riemann解.     

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.     

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.     

高阶广义KDV方程和KP方程的数值解法

采用一种线性隐格式来解3-阶和5-阶的广义Korteweg-De Vries(KDV)方程,对这种方法做一推广,就能应用到它的二维形式广义Kadomtsew-Petviashvili(KP)方程．这种方法是无条件稳定的,且是无损耗的．数值实验描述了一个线性孤波运动的情形以及两个孤波交互的情形,从结果来看,它们满足孤立子解的两个守恒-动量守恒和能量守恒．     

双曲型燃烧模型方程组的Riemann问题

本文研究了一类反应速率有限或反应速率无穷的燃烧模型组的 Riemann问题。作者证明了有限反应率的 Riemann解是由一个激波跟随一有限宽度的反应区构成,而无穷反应率的Riemann 解是由一强爆轰波或由一 Chapmann-Jouget爆轰波跟随一中心稀疏波构成。     

一类变式Boussinesq系统的行波解

本文研究—类变式Boussinesq系统ηt+((1+αη)w)x-β/6wxxx=0, wt+αwwx+ηx-β/2wxxt=0,其中α和β都是正常数.许多逼近模型都能从此系统中被推导出,比如Boussinesq系统和两分量Camassa-Holm系统等.本文利用平面动力系统方法研究它的行波解及相图,得到了孤立波解,广义扭波解,广义反扭波解,紧孤立波解和周期波解,并给出了这些解的数值模拟.     

The generalized Riemann problem for a scalar Chapman–Jouguet combustion model

The generalized Riemann problem for a scalar Chapman–Jouguet combustion model in a neighborhood of the origin (t > 0) on the (x, t) plane is studied. Under the entropy conditions, we obtain the solutions constructively. It is found that, for some cases, the perturbed Riemann solutions are essentially different from the corresponding Riemann solutions. The perturbation may transform a combustion wave CJDT into SDT in the neighborhood of the origin. Especially, it can be observed that burning happens although the corresponding Riemann solution doesn’t contain combustion waves, which exhibits the instability for unburnt states. This work is supported by NSFC 10671120     

Perturbed Riemann Problem for a Scalar Chapman-Jouguet Combustion Model

The author considers the perturbed Riemann problem for a scalar ChapmanJouguet combustion model which comes from Majda’s model with a modified, bump-type ignition function proposed in the results of Lyng and Zumbrun in 2004. Under the entropy conditions, the unique solution in a neighborhood of the origin on the(x, t) plane(t > 0) is obtained. It is found that, for some cases, the perturbed Riemann solutions are essentially different from the corresponding Riemann solutions. The perturbation may transform a strong detonation into a weak deflagration in the neighborhood of the origin. Especially, it can be observed that burning happens although the corresponding Riemann solution does not contain combustion wave, which exhibits the instability for the unburnt state.     

THE GENERALIZED RIEMANN PROBLEM FOR A SCALAR NONCONVEX COMBUSTION MODEL-THE PERTURBATION ON INITIAL BINDING ENERGY

In this article,we study the generalized Riemann problem for a scalar nonconvex Chapman-Jouguet combustion model in a neighborhood of the origin (t ＞ 0) on the (x,t) plane.We focus our attention to the...     

The perturbation on initial binding energy for a Majda-CJ combustion model

We investigate the perturbed Riemann problem for a scalar Chapman–Jouguet combustion model – the perturbation on initial binding energy. Under the entropy conditions, we obtain the unique solutions in a neighbourhood of the origin (t?>?0) on the (x,?t) plane. It is found that, for some cases, the perturbed Riemann solutions are essentially different from the corresponding Riemann solutions. That is, the perturbation may transform a Chapman–Jouguet detonation into a strong detonation or a weak deflagration following a shock wave; a strong detonation into a weak deflagration following a shock wave; a Chapman–Jouguet deflagration into a weak deflagration.     

A HYPERBOLIC SYSTEM OF CONSERVATION LAWS FOR FLUID FLOWS THROUGH COMPLIANT AXISYMMETRIC VESSELS

We are concerned with the derivation and analysis of one-dimensional hyperbolic systems of conservation laws modelling fluid flows such as the blood flow through compliant axisymmetric vessels.Early models derived are nonconservative and/or nonhomogeneous with measure source terms,which are endowed with infinitely many Riemann solutions for some Riemann data.In this paper,we derive a one-dimensional hyperbolic system that is conservative and homogeneous.Moreover,there exists a unique global Riemann solution for the Riemann problem for two vessels with arbitrarily large Riemann data,under a natural stability entropy criterion.The Riemann solutions may consist of four waves for some cases.The system can also be written as a 3×3 system for which strict hyperbolicity fails and the standing waves can be regarded as the contact discontinuities corresponding to the second family with zero eigenvalue.     

Rarefaction Wave Interaction and Shock-Rarefaction Composite Wave Interaction for a Two-Dimensional Nonlinear Wave System

In order to construct global solutions to two-dimensional(2 D for short)Riemann problems for nonlinear hyperbolic systems of conservation laws,it is important to study various types of wave interactions.This paper deals with two types of wave interactions for a 2 D nonlinear wave system with a nonconvex equation of state:Rarefaction wave interaction and shock-rarefaction composite wave interaction.In order to construct solutions to these wave interactions,the authors consider two types of Goursat problems,including standard Goursat problem and discontinuous Goursat problem,for a 2 D selfsimilar nonlinear wave system.Global classical solutions to these Goursat problems are obtained by the method of characteristics.The solutions constructed in the paper may be used as building blocks of solutions of 2 D Riemann problems.     

The singular solutions to a nonsymmetric system of Keyfitz-Kranzer type with initial data of Riemann type

The solutions to the Riemann problem for a nonsymmetric system of Keyfitz-Kranzer type are constructed explicitly when the initial data are located in the quarter phase plane. In particular, some singular hyperbolic waves are discovered when one of the Riemann initial data is located on the boundary of the quarter phase plane, such as the delta shock wave and some composite waves in which the contact discontinuity coincides with the shock wave or the wave back of rarefaction wave. The double Riemann problem for this system with three piecewise constant states is also considered when the delta shock wave is involved. Furthermore, the global solutions to the double Riemann problem are constructed through studying the interaction between the delta shock wave and the other elementary waves by using the method of characteristics. Some interesting nonlinear phenomena are discovered during the process of constructing solutions; for example, a delta shock wave is decomposed into a delta contact discontinuity and a shock wave.     

Limit relations for three simple hyperbolic systems of conservation laws

This paper is concerned with the limit relations from the Euler equations of one‐dimensional compressible fluid flow and the magnetohydrodynamics equations to the simplified transport equations, where the δ‐shock waves occur in their Riemann solutions of the latter two equations. The objective is to prove that the Riemann solutions of the perturbed equations coming from the one‐dimensional simplified Euler equations and the magnetohydrodynamics equations converge to the corresponding Riemann solutions of the simplified transport equations as the perturbation parameterx ε tends to zero. Furthermore, the result can also be generalized to more general situations. Copyright © 2009 John Wiley & Sons, Ltd.