Asymptotic behavior of solutions to the Cauchy problem for 1D <i>p</i> -system with nonlinear damping

This paper investigates the Cauchy problem for the compressible Euler equations with a nonlinear damping term. We establish the global existence of solutions via the timeweighted energy estimate method, by technically constructing correction functions to delete the gaps at far fields, and further derive the L p -estimates by constructing an approximate Green's function, which improves the existing studies.