Homogenization of a quasilinear parabolic equation with vanishing viscosity
Homogenization of a quasilinear parabolic equation with vanishing viscosity
复制标题
具有消失粘度的拟线性抛物线方程的齐次化
DOI：
10.1016/j.matpur.2006.04.001
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Anne
中科院分区：
文献类型：
--
作者：
Anne
研究了方程<$tuε+divx[A（xε，uε）]-εΔxuε=0的解在ε→0时的极限.在计算了均匀化问题之后，由于形式的双尺度展开，我们证明了当ε趋于0时，uε在Lloc 2中表现为v（xε，u <$（t，x）），其中v由单元问题确定，u <$是均匀化问题的解。证明依赖于使用两个尺度的杨措施，杨措施适应两个尺度的均匀化问题的推广。
We study the limit as ε→0 of the solutions of the equation ∂tuε+divx[A(xε,uε)]−εΔxuε=0. After computing the homogenized problem thanks to formal double-scale expansions, we prove that as ε goes to 0, uεbehaves in Lloc2as v(xε,u¯(t,x)), where v is determined by a cell problem and u¯ is the solution of the homogenized problem. The proof relies on the use of two-scale Young measures, a generalization of Young measures adapted to two-scale homogenization problems.