固液两相流中的K-ε双方程湍流模式*

建立了固液两相流中更一般的K-ε双方程湍流模式。模化了固相和液相的连续方程、动量方程及K方程和ε方程。该湍流模型考虑了固液两相间速度的滑移,颗粒间的作用及相间作用。使用本文所建立的湍流模型,数值预测了一管湍流中的沙水混合流动,其预测结果与实验结果比较一致。     

Boltzmann方程的两个解的平均作为二粒子Boltzmann方程系的解

在这篇文章,由Boltzmann方程的两个解构造出二粒子Boltzmann方程系的一类解。利用这个结果,求出了二粒子Boltzmann方程系的平衡解及宏观运动方程组。     

单调算子的值域和在混合边值问题中的应用

通过定义几种算子,对其性质加以研究,并利用了Reich的关于值域和的有关结果,研究了非线性椭圆型方程及非线性抛物型方程,推导出这两种方程的解的存在性条件,从而推广了Pascali的相关结果.     

R~3中一类Kirchhoff型方程变号解的存在性及集中性（英文）

本文研究了一类Kirchhoff型方程.利用极大极小原理及惩罚函数方法,证明了上述方程变号解的存在性及集中性,我们的结果推广了文献[4]的结果.     

二阶时滞Volterra微积分方程数值研究（英文）

本文研究二阶时滞Volterra微积分方程收敛问题.利用勒让德谱方法,获得方程的精确解与近似解及精确导数与近似导数误差在指定范数空间呈指数收敛结果,推广了二阶Volterra方程的结果.     

非线性对流扩散方程的三层隐-显hp-局部间断Galerkin有限元方法

使用Arnold等人提出的求解椭圆方程的间断有限元的一般框架及新的处理非线性对流项的方法,得到了非线性对流扩散方程的三层隐-显hp-LDG方法的误差估计.对Burgers方程进行了数值计算,计算结果验证了文中得到的理论结果.     

一类与Whitehead方程有关的函数方程在群上的解

考虑了一类推广的Whitehead方程,给出了此类方程在自由有群及几种特定群上的解的具体表达式,推广了前人的结果.     

关于矩阵方程XB=C的结构解

很多应用中导出矩阵方程XB=G,本文考虑此方程的结构解.首先考虑自伴矩阵解及反自伴矩阵解,接下来考虑广义对称解及广义反对称解,最后讨论更广泛的矩阵方程AXB=C的酉矩阵解.所得结果推广了Sun,Tisseur,Trench等人的-些结果.     

扰动Boussinesq方程的近似守恒律

构造了具有扰动项的Boussinesq方程的近似守恒向量和近似守恒律.在方程允许拉格朗日函数的情况下,利用欧拉方程的部分拉格朗日函数方法,研究了含有一阶线性组合扰动项的Boussineq方程的近似守恒律.给出了该方程的近似守恒向量及近似守恒律的分类结果.     

关于带有非线性控制项及强迫项的差分方程的周期解

考虑了带有非线性控制函数及强迫项的差分方程,该方程可应用于神经网络的研究中,建立了该方程存在周期解的一个充分条件,表明如何将其周期解构造出来并给出一个具体例子说明这一结果.     

The Kirchhoff type Schrödinger problem with critical growth

In this paper, we study the Kirchhoff type problem with critical growth. By using the variational method, the existence and multiplicity of solutions are obtained.     

ON TRANSMISSION PROBLEM FOR KIRCHHOFF TYPE WAVE EQUATION WITH A LOCALIZED NONLINEAR DISSIPATION IN BOUNDED DOMAIN＊

In this article,we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physically different types of materials,one...     

On transmission problem for viscoelastic wave equation with a localized a nonlinear dissipation

In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physically different types of materials, one component being a Kirchhoff type wave equation with time dependent localized dissipation which is effective only on a neighborhood of certain part of boundary, while the other being a Kirchhoff type viscoelastic wave equation with nonlinear memory.     

带有临界增长的Kirchhoff型问题的基态解

本文主要考虑如下Kirchhoff问题{-(a+b∫R_3|?u|~2dx)?u+u=f(x,u)+Q(x)|u|~4u,u∈H~1(R~3),其中a,b是正的常数.我们证明了基态解,即上述问题的极小能量解的存在性.同时,如果假定Q≡1,且h(x)满足一定的条件,可以证明下述问题{-(a+b∫R_3|?u|~2dx)?u+u=|u|~4u+h(x)u,u∈H~1(R~3)的基态解的存在性.     

Hyperbolic-parabolic singular perturbation for quasilinear equations of Kirchhoff type

We consider a hyperbolic-parabolic singular perturbation problem for a quasilinear equation of Kirchhoff type, and obtain parameter-dependent time decay estimates of the difference between the solutions of a quasilinear dissipative hyperbolic equation of Kirchhoff type and the corresponding quasilinear parabolic equation. For this purpose we show time decay estimates for hyperbolic-parabolic singular perturbation problem for linear equations with a time-dependent coefficient.     

Finite element analysis of parabolic integro-differential equations of Kirchhoff type

The aim of this paper is to study parabolic integro-differential equations of Kirchhoff type. We prove the existence and uniqueness of the solution for this problem via Galerkin method. Semidiscrete formulation for this problem is presented using conforming finite element method. As a consequence of the Ritz–Volterra projection, we derive error estimates for both semidiscrete solution and its time derivative. To find the numerical solution of this class of equations, we develop two different types of numerical schemes, which are based on backward Euler–Galerkin method and Crank–Nicolson–Galerkin method. A priori bounds and convergence estimates in spatial as well as temporal direction of the proposed schemes are established. Finally, we conclude this work by implementing some numerical experiments to confirm our theoretical results.     

Multiple positive solutions for a Kirchhoff type problem with a critical nonlinearity

In this paper, we study the multiplicity results of positive solutions for a Kirchhoff type problem with critical growth, with the help of the concentration compactness principle, and we prove that problem admits two positive solutions, and one of the solutions is a positive ground state solution.     

Asymptotic behavior of solutions for nonlinear wave equations of Kirchhoff type with a positive–negative damping

The initial–boundary value problem of Kirchhoff type with an intermittent damping is considered. Under some appropriate assumptions, we give some sufficient conditions for the asymptotic stability of the solutions.     

Three Solutions of a Kirchhoff Type Problem Involving Critical Growth and Near Resonance

The purpose of this work is to study a Kirchhoff type equation involving critical and singular nonlinearities. Based on variational methods, we obtain the existence of three nontrivial solutions for this problem.     

Existence results for some Kirchhoff-Carrier problems

Analyzing the viscoelastic problem for small vibrations of elastic strings, Kirchhoff and Carrier proposed two different models of nonlinear partial differential equations. By combining these two models, we deal here with some nonlocal hyperbolic problems that cover a large class of Kirchhoff and Carrier type problems. The existence of local solutions of degenerate problems as well as local and nonlocal solutions of nondegenerate problems is established. The proofs are based on the combination of the Schauder fixed point theorem with some asymptotic method.