本项目研究抛物方程及其动力系统的均匀化定量理论，具体如下：（1）利用加权估计、加权对偶方法研究高阶线性抛物方程（组）周期均匀化的收敛速度，进而结合Campanato迭代研究均匀化的一致正则性；（2）利用紧方法研究校正子逼近理论，进而结合Rellich估计、加权估计、非切向极大函数估计以及Campanato迭代，来研究线性抛物方程（组）几乎周期均匀化的收敛速度及一致正则性；（3）利用算子理论、线性抛物方程（组）均匀化理论及无穷维动力系统吸引子理论，研究非线性抛物方程（组）吸引子的周期、几乎周期均匀化的收敛速度及一致正则性。偏微分方程的均匀化理论在物理、工程技术以及材料科学领域有着广泛的应用，是目前偏微分方程及相关领域极为活跃的研究方向。本项目预期结果将进一步丰富和完善偏微分方程均匀化及无穷维动力系统领域现有的理论和结果，并为强非均匀介质及相关问题的数值模拟提供一定的理论指导。

The project is devoted to homogenization theory of parabolic equations and their dynamical systems. More precisely, (1) we use weighted estimates and the weighted duality method to investigate the convergence rate in periodic homogenization of linear higher-order parabolic equations, based on which and proper Campanato iteration method, we explore the uniform regularity in the homogenization; (2) we use the compactness method to study the approximation theory of correctors, then combined with Rellich estimates, weighted estimates, nontangential maximal function estimates and Campanato iteration, we investigate the convergence rate and uniform regularity in almost periodic homogenization of linear parabolic equations; (3) we use the operator theory, homogenization of linear parabolic equations and the theory of attractors to study the convergence rates and uniform regularity estimates in periodic and almost periodic homogenization of attractors for nonlinear parabolic equations. Homogenization of partial differential equations (systems) has wide applications in physics, mechanics, and materials science, which is now a very active research area in partial differential equations. The project will enrich the existing theory and results in homogenization of partial differential equations and infinite dynamical systems, and will provide theoretical foundation for numerical simulations in strongly inhomogeneous materials.