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A 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 \( \varepsilon \), is investigated. Results obtained prove that for slow time \( \varepsilon t <1 \) waves are propagated almost undisturbed, while for fast time \( t>\frac{1}{\varepsilon } \) diffusion effects prevail.

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