A wave equation perturbed by viscous terms: fast and slow times diffusion effects in a Neumann problem

Neumann problem for a wave equation perturbed by viscous terms with small parameters is considered. The interaction of waves with the diffusion effects caused by a higher-order derivative with small coefficient ε , is investigated. Results obtained prove that for slow time ε t <1 waves are propagated almost undisturbed, while for fast time t>1/ε diffusion effects prevail.