On the spectral asymptotics of waves in periodic media with Dirichlet or Neumann exclusions

Summary We consider homogenization of the scalar wave equation in periodic media at finite wavenumbers and frequencies, with the focus on continua characterized by: (a) arbitrary Bravais lattice in \mathbb{R}^d d \geqslant 2 and (b) exclusions, that is, ‘voids’ that are subject to homogeneous (Neumann or Dirichlet) boundary conditions. Making use of the Bloch-wave expansion, we pursue this goal via asymptotic ansatz featuring the ‘spectral...