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

2021/12/20 by Zhang, Nangao, Zhu, Changjiang
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2112.10392

Abstract

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.

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