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In this paper, we are concerned with the asymptotic behavior of solutions ofM1 model on quadrant. From this model, combined with damped compressible Eulerequations, a more general system is introduced. We show that the solutions tothe initial boundary value problem of this system globally exist and tendtime-asymptotically to the corresponding nonlinear parabolic equation governedby the related Darcy's law. Compared with previous results on compressibleEuler equations with damping obtained by Nishihara and Yang in [24], andMarcati, Mei and Rubino in [16], the better convergence rates are obtained. Theapproach adopted is based on the technical time-weighted energy estimatestogether with the Green's function method.

Long-time behavior of solutions to the M1 model with boundray effect