scholarly journals Large time behavior of solutions for a Cauchy problem on a nonlinear conservation law with large initial data in the whole space

2017 ◽  
Vol 41 (4) ◽  
pp. 1388-1409
Author(s):  
Lingyu Jin ◽  
Lang Li ◽  
Shaomei Fang
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Conservation Law ◽  
Large Time ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Large Initial Data ◽  
Whole Space

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

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yusuke Ishigaki
Keyword(s):  
Initial Data ◽  
Large Time ◽  
Three Dimensional ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Viscoelastic System ◽  
Diffusion Wave ◽  
Estimates Of Solutions ◽  
Whole Space ◽  
Wave Phenomena

<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>

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