中文摘要：

研究一类粘性四阶退化抛物方程弱解的存在性问题.在初始函数的一些假定下,首先考虑半离散问题,利用极小元泛函方法证明构造的椭圆方程弱解的存在性;其次构造此粘性四阶退化抛物方程的逼近解,通过选取恰当的检验函数对逼近解的作一致性估计,得到逼近解的收敛性结果,进而获得弱解的存在性.

英文摘要：

The weak solutions of a class of fourth order degenerate parabolic equation are studied. Under some assumptions on the initial value,the first thing is to cosider a discrete problem. By using minimizer functional method,the existence of weak solution to the elliptic equation is proved. Secondly,the approximation solutions of the four order degenerate parabolic equation are constructed. By choosing reasonable test functions to get the necessary uniform estimations,the convergence results can be obtained and then the existence of the weak solutions is proved.