On resonances in a homogenization problem
Rustem Rashitovich Gadyl'shin · Comptes Rendus Mécanique · 2003
We consider a two-dimensional boundary value problem for the Helmholtz equation with Neumann boundary condition on a set of arcs. This set is obtained from a closed curve by cutting out small holes situated closely each to other and having locally periodic structure. We construct asymptotics of scattering frequencies (poles of analytic continuation of solutions) with small imaginary parts and show that these scattering frequencies imply resonances.