Homogenization of periodic systems with large potentials
Consider a system of second order equation in a periodic medium with a large potential (if \(\epsilon\) denotes the period the potential is scaled as \(\epsilon^{-2}\). Under some spectral assumptions on the cell problem the authors prove that the solution can be factorized as a product of a fast oscillating cell eigenfunction and of a slowly varying solution of a scalar second order equation. The result applies to the parabolic case as well as to the hyperbolic one and also to a fourth order plate equation. The methods used are a combination of the two scales convergence method, oscillating test functions methods and Bloch wave decomposition method.
scientific article; zbMATH DE number 2140284
scientific article