Homogenization of a Continuously Microperiodic Multidimensional Medium

Marcos Pinheiro Lima, Leslie Darien Pérez Fernández, Julián Bravo Castillero


The asymptotic homogenization method is applied to obtain formal asymptotic solution and the homogenized solution of a Dirichlet boundary-value problem for an elliptic equation with rapidly os- cillating coefficients. The proximity of the formal asymptotic solution and the homogenized solution to the exact solution is proved, which provides the mathematical justification of the homogenization pro- cess. Preservation of the symmetry and positive-definiteness of the effective coefficient in the homogenized problem is also proved. An example is presented in order to illustrate the theoretical results.

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DOI: https://doi.org/10.5540/tema.2018.019.01.15

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