Citation: |
[1] |
C. M. Dafermos, Can dissipation prevent the breaking of waves? In Transactions of the Twenty-Sixth Conference of Army Mathematicians, ARO Rep. 81, 1, U. S. Army Res. Office, Research Triangle Park, N.C., (1981), 187-198. |
[2] |
R. J. Duan, H. X. Liu, S. Ukai and T. Yang, Optimal $L^p$-$L^q$ convergence rate for the compressible Navier-Stokes equations with potential force, J. Differential Equations, 238 (2007), 220-233.doi: 10.1016/j.jde.2007.03.008. |
[3] |
R. J. Duan, S. Ukai, T. Yang and H. J. Zhao, Optimal convergence rate for the compressible Navier-Stokes equations with potential force, Math. Mod. Meth. Appl. Sci., 17 (2007), 737-758.doi: 10.1142/S021820250700208X. |
[4] |
Y. Guo and Y. J. Wang, Decay of dissipative equations and negative Sobolev spaces, Comm. PDE., 37 (2012), 2165-2208.doi: 10.1080/03605302.2012.696296. |
[5] |
L. Hsiao, Quasilinear Hyperbolic Systems and Dissipative Mechanisms, World Scientific Publishing Co., River Edge, NJ, 1997. |
[6] |
L. Hsiao and T. P. Liu, Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping, Comm. Math. Phys., 143 (1992), 599-605.doi: 10.1007/BF02099268. |
[7] |
F. M. Huang and R. H. Pan, Convergence rate for compressible Euler equations with damping and vacuum, Arch. Ration. Mech. Anal., 166 (2003), 359-376.doi: 10.1007/s00205-002-0234-5. |
[8] |
F. M. Huang, P. Marcati and R. H. Pan, Convergence to the Barenblatt Solution for the Compressible Euler Equations with Damping and Vacuum, Arch. Ration. Mech. Anal., 176 (2005), 1-24.doi: 10.1007/s00205-004-0349-y. |
[9] |
F. M. Huang, R. H. Pan and Z. Wang, $L^1$ convergence to the Barenblatt solution for compressible Euler equations with damping, Arch. Ration. Mech. Anal., 200 (2011), 665-689.doi: 10.1007/s00205-010-0355-1. |
[10] |
M. Jiang and C. J. Zhu, Convergence to strong nonlinear diffusion waves for solutions to p-system with damping on quadrant, J. Differential Equations, 246 (2009), 50-77.doi: 10.1016/j.jde.2008.03.033. |
[11] |
T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Rational Mech. Anal., 58 (1975), 181-205.doi: 10.1007/BF00280740. |
[12] |
S. Kawashima, Systems of a Hyperbolic-Parabolic Composite Type, with Applications to the Equations Of Magnetohydrodynamics, Ph.D thesis, Kyoto University, Kyoto, 1983. |
[13] |
A. J. Majda and A. L. Bertozzi, Vorticity and Incompressible Flow, Cambridge University Press, Cambridge, 2002. |
[14] |
A. Majda, Compressible Fluid Flow and Conservation laws in Several Space Variables, Springer-Verlag, Berlin/New York, 1984.doi: 10.1007/978-1-4612-1116-7. |
[15] |
P. Marcati and A. Milani, The one-dimensional Darcy's law as the limit of a compressible Euler flow, J.Differential Equations, 84 (1990), 129-147.doi: 10.1016/0022-0396(90)90130-H. |
[16] |
A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases, J Math Kyoto Univ, 20 (1980), 67-104. |
[17] |
T. Nishida, Global solutions for an initial-boundary value problem of a quasilinear hyperbolic systems, Proc. Japan Acad., 44 (1968), 642-646.doi: 10.3792/pja/1195521083. |
[18] |
T. Nishida, Nonlinear hyperbolic equations and related topics in fluid dynamics, Publ. Math. D'Orsay, (1978), 46-53. |
[19] |
L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, 13 (1959), 115-162. |
[20] |
T. C. Sideris, B. Thomases and D. H. Wang, Long time behavior of solutions to the 3D compressible Euler equations with damping, Comm. PDE., 28 (2003), 795-816.doi: 10.1081/PDE-120020497. |
[21] |
Z. Tan and G. C. Wu, Large time behavior of solutions for compressible Euler equations with damping in $\mathbbR^{3}$, J. Differential Equations, 252 (2012), 1546-1561.doi: 10.1016/j.jde.2011.09.003. |
[22] |
W. Wang and T. Yang, The pointwise estimates of solutions for Euler equations with damping in multi-dimensions, J. Differential Equations, 173 (2001), 410-450.doi: 10.1006/jdeq.2000.3937. |
[23] |
C. J. Zhu, Convergence rates to nonlinear diffusion waves for weak entropy solutions to p-system with damping, Sci. China Ser. A, 46 (2003), 562-575.doi: 10.1360/03ys9057. |