TWO EXAMPLES OF EFFECTIVE OPERATORS IN THE LONG TIME HOMOGENIZATION OF WAVE SYSTEMS
Grégoire Allaire, Agnes Lamacz-Keymling, Jeffrey B. Rauch · HAL (Le Centre pour la Communication Scientifique Directe) · 2024
This note is a supplementary material for our article [2]. It gives two specific examples of locally periodic systems of wave equations, for which the homogenization results are different from those obtained for a scalar and purely periodic wave equation. The first example shows that the third-order homogenized operator may not vanish for systems, contrary to the scalar case. The second example exhibits a high-order homogenized operator which is not in divergence form for a locally periodic wave equation, contrary to the purely periodic case.