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In this paper, we study the Cauchy problem for a nonlinear wave equation withfrictional and viscoelastic damping terms. As is pointed out by [8], in thiscombination, the frictional damping term is dominant for the viscoelastic onefor the global dynamics of the linear equation. In this note we observe that ifthe initial data is small, the frictional damping term is again dominant evenin the nonlinear equation case. In other words, our main result is diffusionphenomena: the solution is approximated by the heat kernel with a suitableconstant. Our proof is based on several estimates for the corresponding linearequations.

Large time behaivor of global solutions to nonlinear wave equations with frictional and viscoelastic damping terms