Abstract
The present work investigates boundary conditions that modelize the penetration of a time‐harmonic wave into a dissipative obstacle. The exact model is given through a transmission problem that couples the propagations into an absorbing domain and an exterior domain. The conditions arise from an asymptotic analysis of the interior solution whose propagation is studied by using pseudodifferential technics classically involved for the construction of radiation boundary conditions. Herein, first and second‐order conditions are analyzed and some numerical experiments illustrate their validity domain.