Asymptotic homogenization of a problem for a wave equation on a microperiodic medium
Douglas Machado da Silva, Leslie D. Pérez‐Fernández, Alexandre Molter, Julián Bravo‐Castillero · Ciência e Natura · 2024
The asymptotic homogenization method is a mathematical technique that allows studying the physical properties of a microheterogeneous, periodic medium characterized by rapidly oscillating coefficients through a homogeneous medium that is asymptotically equivalent to the micro-heterogeneous medium. The method involves constructing a two-scale formal asymptotic solution of the original problem, and by applying mathematical formalism, a problem is formulated over a homogenized medium known as the homogenized problem. Utilizing maximum principles, it is proven that the solution to the homogenized problem is an asymptotic expansion of the solution to the original problem. This work aims to apply this method to a problem for a hyperbolic equation and demonstrate the proximity between the solutions.