Open AccessHomogenization of a Continuously Microperiodic Multidimensional Medium
Author(s) -
Marcos Pinheiro Lima,
Leslie D. Pérez-Fernández,
Julián Bravo Castillero
Publication year - 2018
Publication title -
tema
Language(s) - English
Resource type - Journals
eISSN - 2179-8451
pISSN - 1677-1966
DOI - 10.5540/tema.2018.019.01.15
Subject(s) - homogenization (climate) , mathematics , asymptotic homogenization , boundary value problem , dirichlet distribution , mathematical analysis , positive definiteness , eigenvalues and eigenvectors , physics , positive definite matrix , biodiversity , ecology , algorithm , quantum mechanics , composite number , biology
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.