Asymptotic homogenization

In mathematics and physics, homogenization is a method of studying partial differential equations with rapidly oscillating coefficients, such as

where ${\displaystyle \epsilon }$ is a very small parameter and ${\displaystyle A\left({\vec {y}}\right)}$ is a 1-periodic coefficient: ${\displaystyle A\left({\vec {y}}+{\vec {e}}_{i}\right)=A\left({\vec {y}}\right)}$, ${\displaystyle i=1,\dots ,n}$.

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