## Optimal decay rates of solutions to hyperbolic conservation laws with damping.(English)Zbl 07461642

Summary: In this paper, we are concerned with the asymptotic behavior of solutions to the system of hyperbolic conservation laws with damping. In particular, a system includes compressible Euler equations with damping, $$M_1$$-model, etc. Under some smallness conditions on initial perturbations, we prove that the solutions to the Cauchy problem of the system globally exist and time-asymptotically converge to corresponding equilibrium state, and further give the optimal convergence rate. The approach adopted is the technical time-weighted energy method combined with the Green’s function method.

### MSC:

 85A25 Radiative transfer in astronomy and astrophysics 35L65 Hyperbolic conservation laws 35B40 Asymptotic behavior of solutions to PDEs 35Q05 Euler-Poisson-Darboux equations 65B15 Euler-Maclaurin formula in numerical analysis 58J47 Propagation of singularities; initial value problems on manifolds 35J08 Green’s functions for elliptic equations 83C40 Gravitational energy and conservation laws; groups of motions
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