均匀化研究是一个数学、力学和材料科学等学科相交叉的课题，它的一个核心内容就是均匀化及其矫正问题的研究。对于穿孔区域中的一类半线性非周期振荡系数的抛物型方程，本项目拟在更弱的条件下，利用穿孔区域Unfolding方法研究其均匀化及其矫正问题。对于带不完美界面区域中的一类非周期振荡系数的双曲型方程，利用二分区域的Unfolding方法，本项目拟研究其均匀化问题；尝试给出一种较以往更弱的且比较自然（即与Unfolding方法相应的）的初值条件，并在此条件下给出矫正结果。特别的，对于特殊情形（即周期振荡系数情形），进一步尝试给出参数等于-1时的矫正结果，这是包括Cioranescu,Damlamian和Donato等著名数学家关心但至今未能解决的问题。这些研究将为全面解决穿孔或带不完美界面区域中的非周期振荡系数的带非齐次边界的非线性发展方程的均匀化问题提供新思路和新方法。

The homogenization theory is a subject interwined with mathematics, mechanics and materials science. The key problem is the homogenization and its corrector results. First, the proposal aims to study a class of semi-linear parabolic equations with non-periodic oscillating coefficients, which are defined in perforated domains. By making use of the unfolding method for perforated domains, the applicant tries to get the homogenization and its corrector results under very weak conditions. The proposal also wants to study a class of hyperbolic equations with non-periodic oscillating coefficients, which are defined in domains with imperfect interfaces. The applicant tries to use the unfolding method for perforated domains to study the homogenization; the applicant also wants to get the corrector results under weaker and more natural conditions. In particular, for the special case, namely, the case with periodic oscillating coefficients, the applicant tries to get the corrector results when the parameter equals to -1. This is a problem many famous mathematicians, including Cioranescu,Damlamian and Donato, want to but do not how to solve.These studies will provide some new ideas and new methods for the study on the homogenization of non-linear evolution equations with non-periodic oscillating coefficients and with non-homogeneous boundary, either for some perforated domains or for some domains with imperfect interfaces.