  In this paper, we are concerned with the asymptotic behavior of solutions of
M1 model on quadrant. From this model, combined with damped compressible Euler
equations, a more general system is introduced. We show that the solutions to
the initial boundary value problem of this system globally exist and tend
time-asymptotically to the corresponding nonlinear parabolic equation governed
by the related Darcy's law. Compared with previous results on compressible
Euler equations with damping obtained by Nishihara and Yang in [24], and
Marcati, Mei and Rubino in [16], the better convergence rates are obtained. The
approach adopted is based on the technical time-weighted energy estimates
together with the Green's function method.
