一类非线性发展方程第一边值问题的有限差分方法

The finite difference method for the first boundary value problem of a class of nonlinear evolution equations

在有限区域上讨论了一类非线性发展方程的第一边值问题，构造了该问题的一类稳定的隐式差分格式，利用离散泛函分析方法得到了差分解的一系列先验估计，由此通过让步长趋于零的极限过程证明了差分格式解的收敛性和原问题的弱解的存在唯一性．

This paper considers the first boundary value problem of a class of nonlinear evolution equations. For this purpose, a stably limplicit difference scheme is constructed. A series of prior estimations of discrete solution are obtained by using the discrete functional analysis method. The convergence of the finite difference schemes, the existence and uniquencess of the weak solution to the original problem are proved by the limiting process in which the steps approaches zero.