On $ L^1 $ estimates of solutions of compressible viscoelastic system

We consider the large time behavior of solutions of compressible viscoelastic system around a motionless state in a three-dimensional whole space. We show that if the initial data belongs to \begin{document}$ W^{2,1} $\end{document}, and is sufficiently small in \begin{document}$ H^4\cap L^1 $\end{document}, the solutions grow in time at the same rate as \begin{document}$ t^{\frac{1}{2}} $\end{document} in \begin{document}$ L^1 $\end{document} due to diffusion wave phenomena of the system caused by interaction between sound wave, viscous diffusion and elastic wave.