Abstract: The initial-regular oblique derivative problem for nonlinear parabolic systems of several second order complex equations with measurable coefficients in a multiply connected domain is discussed. Firstly, the author is a priori estimates of solutions for the above initial-boundary value problem with some conditions, afterwards by using the above estimates of solutions and the method of parameter extension, the existence of solutions for the above problem is proved.

Key words: initial-regular oblique derivative problems, nonlinear parabolic systems, measurable coefficients

摘要： 论述了多连通区域上可测系数的二阶非线性抛物型方程组的初-正则斜微商问题。首先，给出一定条件下的上述初边值问题解的先验估计，然后使用解的上述估计和参数开拓法证明这种初边值问题解的存在性。

关键词: 初-正则斜微商问题, 非线性抛物型方程组, 可测系数