Scattering by Finely Layered Obstacles: Frequency-Explicit Bounds and Homogenization

We consider the scalar Helmholtz equation with variable, discontinuous coefficients, modeling transmission of acoustic waves through an anisotropic penetrable obstacle. first prove a well-posedness result and frequency-explicit bound on solution operator that are valid for sufficiently large frequency class coefficients satisfy certain monotonicity conditions in one spatial direction only assumed to be bounded (i.e., ) other directions. This therefore includes by obstacles (potentially large) number layers (in 2-d) or fibers 3-d). Importantly, holds uniformly all this class; uniformity allows us highly oscillatory study limiting behavior when period oscillations goes zero. In particular, we error committed first-order bulk correction homogenized problem, explicit both equation; best our knowledge, is homogenization these two quantities without assumption small.