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• W4312322489 abstract "In this paper, we are concerned with the asymptotic behavior of solutions of $ M_1 $ model on quadrant $ (x,t) in mathbb{R}^{+} times mathbb{R}^{+} $. 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 [26], and Marcati, Mei and Rubino in [17], 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." @default.
• W4312322489 created "2023-01-04" @default.
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• W4312322489 date "2023-01-01" @default.
• W4312322489 modified "2023-10-05" @default.
• W4312322489 title "Long-time behavior of solutions to the $ M_1 $ model with boundary effect" @default.
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• W4312322489 doi "https://doi.org/10.3934/dcds.2022180" @default.
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