带有可测系数的二阶非线性抛物型方程组的初—混合边值问题

在多连通区域上研究带有可测系数的二阶非线性抛物型方程组的初－混合边值问题，首先我们将其化为复形式的方程组，并给出在一定条件下的上述初－这值问题解的先验估计，然后利用解的估计和列紧性原理，证明了这种初－边值问题解的存在性。在论证过程中，我们始终用复分析方法讨论文中所提出的问题，没有看到国外有人使用这种方法处理此类问题。

INITIAL MIXED BOUNDARY VALUE PROBLEMS FOR NONLINEAR PARABOLIC SYSTEMS OF SEVERAL SECOND ORDER EQUATIONS WITH MEASURABLE COEFFICIENTS

This paper deals with the initial mixed boundary value problem for nonlinear parabolic systems of several second order equations with measurable coefficients in a multiply connected domain, we give a priori estimates of solutions for the above initial boundary value problem with some conditions, and by using the above estimates and the compactness principle of solutions, the existence of solutions for the above problem is proved.