浅水波方程的初边值问题

本文用Kato关于拟线性演化方程的初值问题的存在性定理证明了浅水波方程在半无界直线上初值问题局部解的存在性。用解的先估计证明了整体解的存在性或解的Blow-up性质，并给出了解关于x的渐近估计。     

一类Burgers—BBM型方程的整体强解

本文考虑一类Burgers—BBM型方程的周期边值问题和初值问题。应用Galerkin方法和能量估计证明这些问题整体强解的存在性和唯一性。最后,讨论解当t→∞时的渐近性质。     

ASYMPTOTIC BEHAVIOR OF POSITIVE RADIAL SOLUTIONS FOR THE GENERALIZED EMDEN-FOWLER EQUATION WITH APPLICATION

In this paper, we consider a class of semilinear parabolic differential equation where nonlinear term has local bounded coefficients. Under some assumptions, we get the existence and uniqueness of solution. Terminate to the time variable, we obtain the so called generalized Emden-Fowler equation and the asymptotic behavior of positive radial solutions have been given in all dimensions. At the end of this paper, we give its application to critical branching Brownian motion (also called measure-valued branching processes).     

耗散Camassa-Holm方程的吸引子

本文就一个新的色散水波方程Camassa-Hohn方程的动力学行为进行了研究，讨论了耗散CH方程的解的整体存在，获得了其解半群在H^2中全局吸引子的存在性．     

一类抛物型趋化模型的解的存在性

本文研究了一类抛物型趋化模型的解的存在性问题.利用算子半群理论,Sobolev嵌入定理及不等式技巧对解进行一些重要的先验估计,然后构造压缩映射证明了模型存在局部解.进一步构造迭代估计来说明不可能存在爆破,从而证明全局解的存在.     

ON THE LASOTA-WAZEWSKA MODEL WITH PIECEWISE CONSTANT ARGUMENT

In this article, a delay differential equation with piecewise constant argument is considered; the existence and global attractivity condition ofalmost periodic solution and quasi-periodic solution are obtained.     

PERIODIC BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM OF THE GENERALIZED CUBIC DOUBLE DISPERSION EQUATION

In this article, the existence, uniqueness and regularities of the global generalized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double dispersion equation
utt - uxx - auxxtt ＋ bux4 - duxxt = f（u）xx
are proved, and the sufficient conditions of blow-up of the solutions for the Cauchy problems in finite time are given.     

Global Classical Solutions to the Equations of Two-dimensional MHD Transverse Flow

A new method for constructing the symmetric form for the hyperbolic systems is introduced. Then a new symmetric form of the equations of MHD transverse flow is constructed by adding an additional equation. With this new form, we obtain the local existence of smooth solution including the case that the initial density may tend to the vacuum state at infinity. Furthermore, the uniformly a priori estimation for the classical solutions is established and the global smooth solutions for a kind of initial data are obtained.     

On Smooth Solution for a Nonlinear 5th Order Equation of KdV Type

The existence of global smooth solutions for a nonlinear 5th order equation of KdV type with the periodic boundary condition and initial value condition is proved, we also get the local smooth characterization of the solution for the initial value problem.     

The initial boundary value problem for quasi-linear wave equation with viscous damping

In this paper, the existence and uniqueness of the local generalized solution and the local classical solution for the initial boundary value problem of the quasi-linear wave equation with viscous damping are proved. The nonexistence of the global solution for this problem is discussed by an ordinary differential inequality. Finally, an example is given.     

退化时滞微分方程的周期解问题

本文讨论退化时滞微分方程的周期解问题．特别地，我们给出二维退化滞后微分方程的周期解的存在性问题，并在最后举例说明其应用。     

广义超弹性杆方程关于Neumann问题解的存在性

通过对广义超弹性杆方程的Neumann边界条件及初始条件的研究,得到了广义超弹性杆方程在Neumann边界条件下局部解和整体解的存在.     

ON THE CAUCHY PROBLEM OF TRANSPORTATION EQUATIONS

1.IntroductionInthepreselltpaper,weconsiderthetransportationsystemwithinitialdatawherepanduaredensityandvelocityrespectively.Thesystemofconservationlaws(1.1)describesthefluidmechanicswithconstalltpressuxe,whichisusedinplasmaphysicswherepressureisassumedtobeaconstant.Thissystemisnon--strictlyhyperbolicwithadoubleeigenvalueAl~AZ=albothAl,AZbeinglinearlydegenerate.AndtheCauchyproblemforthissystemisnotwell-posedintheclassofmeasurableandboundedfunctions(see[3]).Inthepresentpaper,weintroduceanew…     

一类广义Sine—Gordon方程的解的存在唯一性

本文利用非线性Ｇａｌｅｒｋｉｎ方法,证明了一类广义Ｓｉｎｅ－Ｇｏｒｄｏｎ方程在Ｄｉｒｉｃｈｌｅｔ边值条件下的整体解的存在唯一性．     

具扰动项的时滞Logistic方程的周期解

本文首先讨论一类时滞微分方程的周期解的存在性，然后将本文结果应用到具扰动项的 时滞Ｌｏｇｉｓｔｉｃ方程得出其正周期解的存在性，本文结果推广和改进了「１」和「６」的相应结果。     

不稳定型二阶中立型方程正解的存在性与有界振动

本文研究一类不稳定型二阶中立型微分方程正解的存在性与有界振动．证明了在一定条件下不稳定型二阶中立型方程总存在无界正解，并给出了保证其方程的一切有界解都振动的充分条件，改进了文［１，２］中的有关条件．     

一类非线性积分微分方程解及其构造

本文讨论了核反应堆动力学中一类具缓发中子的非线性积分微分方程．在一定的条件下证明了该方程在p空间中Mild解、强解、局部解的存在唯一性，以及用迭代法求解的合理性，并估计了收敛速度．     

Global existence and asymptotic dynamics in a 3D fractional chemotaxis system with singular sensitivity

In this paper, we investigate the global existence and asymptotic dynamics of solutions to a fractional singular chemotaxis system in three dimensional whole space. We deal with the new difficulties arising from fractional diffusion by using Riesz transform and Kato-Ponce’s commutator estimates appropriately, and establish the local existence of solution. Then with the help of combining the local existence and the a priori estimates, the global existence and uniqueness of solution with small initial data is derived. Moreover, we obtain the asymptotic decay rates of solution by the method of energy estimates.     

THE EXISTENCE AND STABILITY OF ALMOST PERIODIC SOLUTION

By using the ordinary dichotomy and theory of stability,we study the nonli- near differential equation and obtain some sufficient conditions which guarantee the existence and stability of almost periodic solution for the nonlinear diffe- rential equation.     

人口动力学中一类含时滞周期反应—扩散方程的正周期解分歧

本文研究人口动力学中一类含时滞周期反应-扩散方程的正周期解问题;利用紧算子的全局分歧结果给出了这个方程正周期解存在的充分必要条件。