一类非线性高阶波动方程的初边值问题

该文研究一类非线性高阶波动方程u_tt－a_1^Uxx+a_₂u_x4+a₃u_x4_tt=φ(u_{x ⁾}x+f(u,u_x,u_xxu_xxx,u_x4)的初边值问题.证明整体古典解的存在唯一性并给出古典解爆破的充分条件.     

Boussinesq型方程的周期边界问题与初值问题的解的存在性

本文研究“坏的Ｂｏｕｓｓｉｎｅｓｑ型方程ｕｔｔ－ｂｕｘｘｘ＝σ（ｕ）ｘｘ的周期边界问题与初值问题的解的存在性问题，其中ｂ〉０为常数，证明了在相当宽松的条件下，上述问题存在局部广义解。     

具间断系数非线性抛物型方程初值问题解的渐近性质

关于二阶线性和非线性抛物型方程初值问题解的渐近性质不少作者做过研究,辜联昆最早研究了具间断系数二阶线性和拟线性抛物型方程初值问题解的渐近性质.李名德和秦禹春以及张立龙做了改进和推广,但是他们讨论的间断面仅限于直线或平面。本文利用中的思想讨论间断面为柱面的具间断系数非线性抛物型方程初值问     

一类非线性四阶波动方程的位势井方法

该文讨论非线性波动方程u_{tt}+u_{xxxx}=σ(u_x)_x+f(x,t)的初边值问题.证明了整体弱解的存在性,还证明了整体广义解的存在唯一性和整体古典解的存在唯一性.     

Initial value problem for a class of nonlinear pseudo-hyperbolic equations

The existence of global weak solutions to the periodic boundary problem or the initial value problem for the nonlinear Pseudo-hyperbolic equation u_(tt)-[a_1+a_2(u_x)~(2m)]u_(xx)-a_3u_(xxt)=f(x,t,u,u_x) is proved by the method of the vanishing of the additional diffusion terms, Leray-Schauder's fixedpoint argument and Sobolev's estimates,where m≥1 is a natural number and a_i>0(i=1,2,3)are constants.     

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.     

一类高阶非线性波动方程的时间周期问题

本文利用临界点理论证明一类高阶非线性波动方程时间周期弱解的存在性．     

广义Ginzburg-Landau型非线性高阶抛物方程的Caucky问题

本文证明了广义Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ型非线性高阶抛物方程的周期边值问题和Ｃａｎｃｈｙ问题广义解和古典解的整体存在性和正则性，并且还证明了解的唯一性和这些解的渐近性质．     

Initial value problem for a class of fourth-order nonlinear wave equations

In this paper, existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractional order Sobolev space using the contraction mapping principle and the extension theorem. The sufficient conditions for the blow up of the solution to the initial value problem are given.