Abstract: This paper deals with the initial-mixed boundary value problem for nonlinear parabolic equations of second order with measurable coefficients in a multiply connected domain. Firstly, we give 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 compactness principle of solutions, the existence of solutions for the above problem is proved. Here the condition (1.4) is weaker than the corresponding condition in [1] and [4], i.e. the constant 4/3 in [1] and [4] is replaced by 3/2 in (1.4).

Key words: initial-mixed problems, parabolic equations, measura-ble coefficients

摘要： 本文处理多连通区域上具有可测系数的二阶非线性抛物型复方程的初。混合边值问题。文中先给出了一定条件下上述初。边值问题解的先验估计，然后用上述解的估计及解序列的列紧性原理证明了以上初－混合问题解的存在唯一性。这里，条件(1.4)较弱于参考文献[1]和[4]中相应的条件，即[1]和[4]中的常数4/3由本文(1.4)式中的常数3/2来代替。

关键词: 初－混合边值问题, 非线性抛物型方程, 可测系数