1<γ<6/5时欧拉-泊松方程组平衡解的存在性

可压缩的欧拉-泊松方程组描述的是具有自引力势能的气态星体内部气体的运动发展规律,它由质量守恒方程、动量守恒方程、能量守恒方程及自引力位势满足的泊松方程构成.该文主要研究质量守恒和能量守恒的情况下方程组的平衡解.在绝热常数1γ6/5和熵函数满足一定的光滑性条件下,引用变量变换将方程组转化成一个半线性椭圆型方程,通过一个类似于Pohozaev等式的恒等式证明了平衡解的存在性.     

带自由边界的可压缩欧拉与欧拉-泊松方程组径向对称解的爆破北大核心CSCD

本文在R^(N)(N=2,3)中研究描述流向外部真空的可压缩流体的欧拉与欧拉-泊松方程组径向对称解的爆破.在分离流体与真空的连续自由边界条件下考虑其自由边值问题.对于径向对称的欧拉方程组,证明若初始流平均向外流动,则其光滑解将在有限时刻爆破.对于带有斥力与弛豫项的单极与双极径向对称欧拉-泊松方程组,证明若某个与初始动量有关的加权泛函适当大,则其光滑解将在有限时刻爆破。     

带非线性阻尼项的欧拉——泊松方程组径向对称解的爆破问题

研究了N维空间中带非线性阻尼项的欧拉-泊松方程组的径向对称解的爆破问题.当t≥0时,定义了泛函H(t)和测试函数φ(r),采用积分法得到了当H(0)满足一定条件时在非光滑边界条件下方程组的非平凡径向对称解将在有限时间内发生爆破.采用相似的方法也得到了一维空间中径向对称解的相应结论.     

带周期位势平面薛定谔-泊松方程组的结点解

利用临界点理论中的亏格定理和Nehari流形技巧,本文证明了在二维全空间上一类带周期位势的薛定谔-泊松方程组高能量解的存在性,且该解存在无穷多个结点区域.更进一步,得到了其基态解的存在性且是不变号的.     

具有球对称结构的相对论欧拉方程组稳态解的存在性

对于等温气体,作者将考虑具有球对称结构的相对论欧拉方程组经典稳态解(定理1.1)和弱稳态解(定理1.2)的存在性.通过求解两个常微分方程以及比较马赫数M和1的关系,定理1.1证明了相对论欧拉方程组经典稳态解的存在性.在一个C~(2,α),α∈(0,1)稳态背景解的扰动下,定理1.2将证明高维球对称跨音速(双曲-椭圆)解的存在性.     

一类平面薛定谔-泊松方程组孤立波的存在性（英文）

本文讨论一类平面薛定谔-泊松方程组孤立波解的性质.利用广义畴数理论和Nehari流形技巧,证明其高能量孤立波解存在无穷结点区域,且基态孤立波解是不变号的.     

数学年刊第27卷B辑第5期(2006)目次和提要

非齐次相对论欧拉方程组柯西问题的整体熵解李亚纯王安娇对理想流体的2×2非齐次相对论欧拉方程组进行了分析,对低阶源项提出了适当的条件,并在这些条件下建立了柯西问题整体熵解的存在性．     

比率依赖型捕食者-食饵系统行波解的存在性

本文讨论一类比率依赖型捕食者 -食饵系统的反应扩散方程组 .首先 ,我们证明了时间周期定常解的存在性和稳定性 .其次 ,我们给出了扩散引起正常数平衡解失稳的条件 .最后 ,我们证明了比率依赖型捕食者 -食饵系统行波解的存在性和渐近性 .     

一维半导体流体动力学模型的局部有界解

本文讨论了能量方程是压力一密度关系的一维半导体流体动力学模型方程,通过把欧拉－泊松方程变成拟线性波动方程,利用拟线性波动方程的局部解存在性,得到一维半导体流体动力学模型的局部解,并且解是有界的。     

共振情况下一类半线性波动方程广义解的存在唯一性

利用全局反函数定理和Galerkin方法,考虑了一类半线性波动方程组广义解的存在性,在非线性项f(t,x,u)满足共振的条件下,得到了方程组解的存在唯-性结果.     

离子声波方程的初值问题

本文讨论由Ott E.等建立的机械模型,并给出了该模型初值问题存在整体性弱解的证明。     

Hammerstein方程的可解定理和解集的性状

本文在ｆ（ｘ，ｕ）关于｜ｕ｜的非常系数非线性控制下研究Ｈａｍｍｅｒｓｔｅｉｎ方程的可解性和解集的性状．     

An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation AXB=C

An iteration method is constructed to solve the linear matrix equation AXB=C over symmetric X. By this iteration method, the solvability of the equation AXB=C over symmetric X can be determined automatically, when the equation AXB=C is consistent over symmetric X, its solution can be obtained within finite iteration steps, and its least-norm symmetric solution can be obtained by choosing a special kind of initial iteration matrix, furthermore, its optimal approximation solution to a given matrix can be derived by finding the least-norm symmetric solution of a new matrix equation . Finally, numerical examples are given for finding the symmetric solution and the optimal approximation symmetric solution of the matrix equation AXB=C.     

Bifurcations and exact traveling wave solutions of the equivalent complex short-pulse equations

In this paper, we study the traveling wave solutions for a complex short-pulse equation of both focusing and defocusing types, which governs the propagation of ultrashort pulses in nonlinear optical fibers. It can be viewed as an analog of the nonlinear Schrodinger (NLS) equation in the ultrashort-pulse regime. The corresponding traveling wave systems of the equivalent complex short-pulse equations are two singular planar dynamical systems with four singular straight lines. By using the method of dynamical systems, bifurcation diagrams and explicit exact parametric representations of the solutions are given, including solitary wave solution, periodic wave solution, peakon solution, periodic peakon solution and compacton solution under different parameter conditions.     

矩阵方程AXB=D解的研究

给出了矩阵方程AXB=D相容的又一充要条件,同时讨论它的极小范数解、最小二乘解和极小范数最小二乘解,推广了文献[1]和[3]的结论.     

Explicit soliton solutions of the Kaup-Kupershmidt equation through the dynamical system approach

In this paper, we study the traveling wave solutions of&nbsp;the Kaup-Kupershmidt (KK)&nbsp;equation through using the dynamical system approach, which is an integrable fifth-order&nbsp;wave equation. Based on Cosgrove's work [3] and the phase analysis method of dynamical&nbsp;systems, infinitely many soliton solutions are presented in an explicit form. To guarantee&nbsp;the existence of soliton solutions, we discuss the parameters range as well as geometrical&nbsp;explanation of soliton solutions.     

On the implementation of the L-Nash bargaining solution in two-person bargaining games

The “Nash program” initiated by Nash (Econometrica 21:128–140, 1953) is a research agenda aiming at representing every axiomatically determined cooperative solution to a game as a Nash outcome of a reasonable noncooperative bargaining game. The L-Nash solution first defined by Forgó (Interactive Decisions. Lecture Notes in Economics and Mathematical Systems, vol 229. Springer, Berlin, pp 1–15, 1983) is obtained as the limiting point of the Nash bargaining solution when the disagreement point goes to negative infinity in a fixed direction. In Forgó and Szidarovszky (Eur J Oper Res 147:108–116, 2003), the L-Nash solution was related to the solution of multiciteria decision making and two different axiomatizations of the L-Nash solution were also given in this context. In this paper, finite bounds are established for the penalty of disagreement in certain special two-person bargaining problems, making it possible to apply all the implementation models designed for Nash bargaining problems with a finite disagreement point to obtain the L-Nash solution as well. For another set of problems where this method does not work, a version of Rubinstein’s alternative offer game (Econometrica 50:97–109, 1982) is shown to asymptotically implement the L-Nash solution. If penalty is internalized as a decision variable of one of the players, then a modification of Howard’s game (J Econ Theory 56:142–159, 1992) also implements the L-Nash solution.     

An axiomatization of the egalitarian solutions

The egalitarian solutions for general cooperative games which were defined and axiomatized by Kalai and Samet, are compared to the Harsanyi solution. It is shown that axioms used by Hart to characterize the Harsanyi solution can be used to characterize the (symmetric) egalitarian solution. The only changes needed are the omission of the scale covariance axiom and the inclusion, in the domain of the solution, of games which lack a certain smoothness requirement.     

关于Burgers-Fisher方程平衡解的分岔问题(英文)

当参数λ在临界值λk=k2(k=1,2,…)附近且小于它时,利用Liapunov-Schmidt方法在奇函数空间H1中得到了两个严格的非平凡定态解,在整个空间H1中得到了一个分岔圆.     

Postoptimal analysis of the multicriteria combinatorial median location problem

We consider a multicriteria variant of the well-known combinatorial minisum facility location problem (median problem) with Pareto and lexicographic optimality principles. Necessary and sufficient conditions of a solution stability to the initial data perturbations in such problems are formulated in terms of binary relations. Numerical examples are given.