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Long-time behavior of solutions to the $ M_1 $ model with boundary effect

  • *Corresponding author: Changjiang Zhu

    *Corresponding author: Changjiang Zhu

The second author is supported by the National Natural Science Foundation of China #12171160, 11771150, 11831003 and the Guangdong Provincial Key Laboratory of Human Digital Twin #2022B1212010004

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  • 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.

    Mathematics Subject Classification: Primary: 85A25, 35L65; Secondary: 35B40.

    Citation:

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