论文标题
具有局部周期性系数的抛物线系统均质化的收敛速率
Convergence rates in homogenization of parabolic systems with locally periodic coefficients
论文作者
论文摘要
在本文中，我们研究了具有局部周期性（在时空和时间）系数的二阶抛物线系统的定量均质化。 $ o（\ varepsilon）$ scale-scale-scale-clis-indraniant错误估计在$ l^2（0，t; l^{\ frac {\ frac {2d} {d-1}}}}（ω））$中以$ c^{1，1，1} $ cylinders在该系数的最低平滑性条件下以$ c^{1，1，1，1}建立。此过程依赖于平滑操作员的关键估计。我们还以抛物线方式开发了新的通量校正器的结构，并对时间边界层进行了清晰的估计。
In this paper we study the quantitative homogenization of second-order parabolic systems with locally periodic (in both space and time) coefficients. The $O(\varepsilon)$ scale-invariant error estimate in $L^2(0, T; L^{\frac{2d}{d-1}}(Ω))$ is established in $C^{1, 1}$ cylinders under minimum smoothness conditions on the coefficients. This process relies on critical estimates of smoothing operators. We also develop a new construction of flux correctors in the parabolic manner and a sharp estimate for temporal boundary layers.
