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

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M2">\begin{document}$ W^{2,1} $\end{document}</tex-math></inline-formula>, and is sufficiently small in <inline-formula><tex-math id="M3">\begin{document}$ H^4\cap L^1 $\end{document}</tex-math></inline-formula>, the solutions grow in time at the same rate as <inline-formula><tex-math id="M4">\begin{document}$ t^{\frac{1}{2}} $\end{document}</tex-math></inline-formula> in <inline-formula><tex-math id="M5">\begin{document}$ L^1 $\end{document}</tex-math></inline-formula> due to diffusion wave phenomena of the system caused by interaction between sound wave, viscous diffusion and elastic wave.</p>