可压缩的Navier—Stokes方程H^2强解的整体存在性

该文对于三维可压缩的Navier-Stokes方程，当其具有小扰动初值时，证明了H2（R3）强解的整体存在性．     

具非齐次线性部分的高阶非线性抛物型方程组的初值问题

本文讨论线性部分为非齐次的高阶非线性抛物型偏微分方程组整体经典解的存在性，得到了这类问题对小初值而言存在整体经典解的一些充分条件．     

非等熵Chaplygin气体极限黎曼解 关于扰动的依赖性

主要研究了非等熵Chaplygin气体黎曼问题初值扰动后解的结构,分析了经典的黎曼问题和扰动问题解的结构及极限结构,发现后者的极限解在δ质量权趋于零时不同于前者解的结构.该结果表明对非等熵Chaplygin气体而言,经典的黎曼问题与带δ初值的黎曼问题有着本质的区别.     

具耗散项的拟线性双曲型方程组柯西问题的整体经典解

本文讨论一般形式的具非线性非严格对角占优耗散项的对角型非严格双曲型微分方程组的柯西问题，在初值Ｃ~１模充分小的假设下，得到了整体经典解的存在性．比较了几个熟知的耗散项条件．     

具耗散项的完全非线性波动方程的经典解

本文利用整体迭代法讨论了具耗散项的完全非线性波动方程具小初值的柯西问题的经典解的存在性及生命跨度的下界估计．     

可压缩活性液晶模型的解的存在性（英文）

本文研究了基于Q-张量框架的可压缩活性液晶模型的流体动力学问题.在全空间或者圆环上,我们证明了模型的大初值局部经典解的存在性.并且，在一定的系数假设下,我们给出了在常数态附近圆环上小初值全局经典解的存在性.     

带群集耗散项的零压流方程的扰动黎曼问题

该文通过分析带群集耗散项的零压流方程初始波含狄拉克激波的波的相互作用,研究了其初值含三片常值和初值含狄拉克测度的两种扰动黎曼问题.当初值为三片常值时,通过广义Rankine-Hugoniot条件和广义熵条件,该文构造性地得到了整体解.进一步地,利用弱解的稳定性理论,通过分析初值为三片常值情形下解的结构并取极限,该文得到了初值含狄拉克测度的扰动黎曼问题的整体解.另外,在构造解的过程中,还引入了一种新的非经典解:狄拉克接触间断解.     

带粘性含不活泼项Cahn-Hilliard方程解的存在性

本文研究了带粘性的含不活泼项Cahn-Hilliard方程柯西问题.利用格林函数不同频域的详细分析及不动点原理,得到了方程大初值情形经典解的整体存在性,推广了以往工作集中在弱解或拟强解或小初值情形下的经典解.     

高阶非线性抛物型偏微分方程组的初值问题

本文讨论一般自治型高阶非线性抛物型偏微分方程组初值问题整体解的存在性，得到了这类问题对小初值存在整体经典解的充分条件。     

一类非严格双曲型守恒律整体连续解的存在性

该文利用初值扰动法，讨论了一类非严格双曲型守恒律Ｃａｕｃｈｙ问题整体连续解的存在性．这类方程包括了等熵气体动力学方程组．一个典型的变形方程组，弹性力学方程组，二次流守恒律和旋转退化方程等有意义的模型．     

On Bounded Solutions of the Emden-Fowler Equation in a Semi-cylinder

Bounded solutions of the Emden-Fowler equation in a semi-cylinder are considered. For small solutions the asymptotic representations at infinity are derived. It is shown that there are large solutions whose behavior at infinity is different. These solutions are constructed when some inequalities between the dimension of the cylinder and the homogeneity of the nonlinear term are fulfilled. If these inequalities are not satisfied then it is proved, for the Dirichlet problem, that all bounded solutions tend to zero and have the same asymptotics as small solutions.     

Asymptotic expansions of solutions to inverse problems for a hyperbolic equation with a small parameter multiplying the highest derivative

Two inverse problems for a hyperbolic equation with a small parameter multiplying the highest derivative are considered. The existence and uniqueness of their solutions are proved. As the small parameter tends to zero, the solutions of the inverse problems are proved to converge to solutions of inverse problems for a parabolic equation.     

A singular perturbation approach for a reaction diffusion system arising in nuclear reactor theory

The qualitative behavior of the solutions of a reaction-diffusion system arising in the theory of nuclear reactors is investigated by means of singular perturbation techniques, the small parameter ? representing the inverse of neutron velocity. At the lowest approximation for small ? the solutions exhibit oscillations about the unique strictly positive equilibrium, much as in the case of the associated lumped parameter system. A two-times representation for solutions of small amplitudes is also given.     

A new model for electrostatic MEMS with two free boundaries

A moving boundary problem with two free boundaries modeling a two-dimensional idealized MEMS device with pull-in instability is discussed. We use a fixed point argument to show that the model possesses stationary solutions for small source voltages. We also give a rigorous evidence that solutions of the model converge towards solutions of the associated small aspect ratio equation in the vanishing aspect ratio limit.     

Multiple solutions for the laminar flow in a porous pipe with suction at slowly expanding or contracting wall

In this paper, the asymptotic solution for the similarity equation of the laminar flow in a porous pipe with suction at expanding and contracting wall has been obtained using the singular perturbation method. However, this solution neglects exponentially small terms in the matching process. To take into account these exponentially small terms, a method involving the inclusion of exponentially small terms in a perturbation series was used to find the two solutions analytically. The series involving the exponentially small terms and expansion ratio predicts dual solutions. Furthermore, the result indicates that the expansion ratio has much important influence on the solutions. When the expansion ratio is zero, it is a special case that Terrill has discussed.     

一类含有分数阶导数的二自由度耦合系统

研究了一类含有小扰动具有分数阶导数的二自由度耦合振子的振动问题.首先对含有由Riemann Liouville定义的分数阶导数的振动方程组构造渐近解,利用多重尺度法,得到振动问题的可解性条件.然后在可解性条件下,得到分数阶指数、系数及小参数对振动的影响,并求得渐近解.最后研究了该解的稳定性,发现定常解都是稳定的     

Decay and scattering of solutions for a generalized Boussinesq equation

In this paper, we consider the long-time behavior of small solutions of the Cauchy problem for a generalized Boussinesq equation. A scattering operator and the nonlinear scattering for small amplitude solutions of the Boussinesq equation are established under certain hypotheses.     

Stationary Boltzmann's Equation With a Source Term

Stationary problems for the nonlinear Boltzmann equation with a source term in a three dimensional rectangular domain with specularly reflecting boundaries are considered. It is proved that these problems possess unique solutions close to equilibrium provided a source term is sufficiently small. It is also shown that the solutions are asymptotically stable under small perturbations as solutions of the time dependent Boltzmann equation.     

Life-span of classical solutions to hyperbolic geometry flow equation in several space dimensions

In this article, we investigate the lower bound of life-span of classical solutions of the hyperbolic geometry flow equations in several space dimensions with “small” initial data. We first present some estimates on solutions of linear wave equations in several space variables. Then, we derive a lower bound of the life-span of the classical solutions to the equations with “small” initial data.     

横向剪变形对具有一小圆孔的浅壳应力集中系数的影响

本文导出了分析计及横向剪变形的浅壳小孔应力集中问题的简化方程.对浅球壳和圆柱壳带一小圆孔的情况,获得了方程的级数形式通解.对均匀内压作用下的圆柱壳,求得了小圆孔边上应力集中系数的近似显式解,并计算了数值结果.