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For the compressible Euler equations with time-dependent damping − 1 (1 + t) λ ρ u , we propose a time asymptotic expansion around the self-similar solution of the generalized porous media equation and rigorously justify this expansion as λ ∈ (1 7 , 1). Furthermore, the above expansion is the best asymptotic profile of the solution to the compressible Euler equations with time-dependent damping. [ABSTRACT FROM AUTHOR]

This paper is concerned with the asymptotic behavior of the solution for quasilinear hyperbolic equations with nonlinear damping. The main novelty in this paper is that we obtain the L(2 ≤ p ≤ +∞) convergence rates of the solution to the quasilinear hyperbolic equations, and we need none of the additional technical assumptions for the nonlinear damping f( v) given by Li and Saxton (Q Appl Math 61:295-313, ). [ABSTRACT FROM AUTHOR]