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In this report we obtain higher order asymptotic expansions of solutions towave equations with frictional and viscoelastic damping terms. Although thediffusion phenomena are dominant, differences between the solutions we dealwith and those of heat equations can be seen by comparing the second orderexpansions of them. In order to analyze such effects we consider the weightedL1 initial data. We also give some lower bounds which show the optimality ofobtained expansions.

Moment conditions and lower bounds in expanding solutions of wave equations with double damping terms