中文摘要：

给出强退化抛物方程u/t=ΔA（u）＋N∑i=bi（u）/ti初边值问题一种边值（BV）弱解的新定义,并通过抛物正则化方法得到解的存在性,利用Kruzkov’s双变量的方法得到解的稳定性.

英文摘要：

We gave a new definition of boundary value （BV） weak solutions of the initial boundary value problem to a strongly degenerate parabolic equation u/t=ΔA（u）＋N∑i=1bi（u）/ti.and obtained the existence of the solution by using the parabolic regularization method. The stability of the solutions was obtained by using Kruzkov bi-variables method.