论文标题
与界面的抛物线均质化
Parabolic Homogenization with an Interface
论文作者
论文摘要
本文以差异形式考虑了二阶抛物线方程的家族，并具有迅速振荡和时间依赖的周期性系数和两个周期性结构之间的接口。在Blanc，Le Bris和Lions启动的框架之后，以及Josien界面的椭圆形均匀化的一般性两尺度扩展，我们可以确定有效的（或同质化的）方程，系数矩阵在界面跨界面进行分散和不连续。此外，我们以$ l^{2（d+2）/{d+2）/{d}} _ {x，t} $获得$ o（\ varepsilon）$收敛速率，并通过$ \ varepsilon $ -smooth方法和统一的内部lipschitz估计，通过紧凑型参数。
This paper considers a family of second-order parabolic equations in divergence form with rapidly oscillating and time-dependent periodic coefficients and an interface between two periodic structures. Following a framework initiated by Blanc, Le Bris and Lions and a generalized two-scale expansion in divergence form of elliptic homogenization with an interface by Josien, we can determine the effective (or homogenized) equation with the coefficient matrix being piecewise constant and discontinuous across the interface. Moreover, we obtain the $O(\varepsilon)$ convergence rates in $L^{2(d+2)/{d}}_{x,t}$ with $\varepsilon$-smoothing method and the uniform interior Lipschitz estimates via compactness argument.
