ZHANG Ying-Hui , WU Guo-Chun . GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR THE 3D COMPRESSIBLE NON–ISENTROPIC EULER EQUATIONS WITH DAMPING[J]. Acta mathematica scientia, Series B, 2014 , 34(2) : 424 -434 . DOI: 10.1016/S0252-9602(14)60016-3

[1] Dafermos C M. Can dissipation prevent the breaking of waves?//Transactions of the Twenty-Sixth Confer-ence of Army Mathematicians, 187-198, ARO Rep 81, 1. Research Triangle Park, NC: US Army Res Office, 1981

[2] Duan R J, Ma H F. Global existence and convergence rates for the 3-D compressible Navier-Stokes equations without heat conductivity. Indiana Univ Math J, 2008, 57(5): 2299–2319

[3] Duan R J, Ukai S, Yang T, Zhao H J. Optimal L^p−L^q convergence rate for the compressible Navier-Stokes equations with potential force. J Differ Equations, 2007, 238: 220–223

[4] Duan R J, Ukai S, Yang T, Zhao H J. Optimal convergence rate for compressible Navier-Stokes equations with potential force. Math Models Methods Appl Sci, 2007, 17: 737–758

[5] Evans L C. Partial Differential Equations. Amer Math Soc, 1998

[6] Fang D Y, Xu J. Existence and asymptotic behavior of C1 solutions to the multi-dimensional compressible Euler equations with damping. Nonlinear Analysis, 2009, 70: 244–261

[7] Hsiao L. Quasilinear Hyperbolic Systems and Dissipative Mechanisms. Singapore: World Scientific, 1998

[8] Hsiao L, Liu T P. Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conser-vation laws with damping. Comm Math Phys, 1992, 143: 599–605

[9] Hsiao L, Liu T P. Nonlinear diffusive phenomena of nonlinear hyperbolic systems. Chinese Ann Math Ser B, 1993, 14: 1–16

[10] Hsiao L, Luo T. Nonlinear diffusive phenomena of solutions for the system of compressible adiabatic flow through porous media. J Differ Equations, 1996, 125: 329–365

[11] Hsiao L, Pan R H. Initial-boundary value problem for the system of compressible adiabatic flowt hrough porous media. J Differ Equations, 1999, 159: 280–305

[12] Hsiao L, Pan R H. The damped p-system with boundary effects. Contemporary Mathematics, 2000, 255: 109–123

[13] Hsiao L, Serre D. Global existence of solutions for the system of compressible adiabatic flow through porous
media. SIAM J Math Anal, 1996, 27: 70–77

[14] Huang F M, Marcati P, Pan R H. Convergence to Barenblatt Solution for the Compressible Euler Equations with Damping and Vacuum. Arch Ration Mech Anal, 2005, 176: 1–24

[15] Huang F M, Pan R H. Asymptotic behavior of the solutions to the damped compressible Euler equations with vacuum. J Differ Equations, 2006, 220: 207–233

[16] Huang F M, Pan R H. Convergence rate for compressible Euler equations with damping and vacuum. Arch Ration Mech Anal, 2003, 166: 359–376

[17] Jiang M N, Ruan L Z, Zhang J. Existence of global smooth solution to the initial boundary value problem for p-system with damping. Nonlinear Anal, 2009, 70(6): 2471–2479

[18] Jiang M N, Zhu C J. Convergence rates to nonlinear diffusion waves for p-system with nonlinear damping on quadrant. Discrete Contin Dyn Syst, 2009, 23(3): 887–918

[19] Jiang M N, Zhu C J. Convergence to strong nonlinear diffusion waves for solutions to p-system with damping on quadrant. J Differ Equations, 2009, 246(1): 50–77

[20] Liu T P. Compressible flow with damping and vacuum. Japan J Appl Math, 1996, 13: 25–32

[21] Marcati P, Milani A. The one-dimensional Darcy’s law as the limit of a compressible Euler flow. J Differ Equations, 1990, 84(1): 129–147

[22] Marcati P, Rubino B. Hyperbolic to Parabolic Relaxation Theory for Quasilinear First Order Systems. J Differ Equations, 2000, 162(2): 359–399

[23] Marcati P, Pan R H. On the diffusive profiles for the system of compressible adiabatic flow through porous media. SIAM J Math Anal, 2001, 33: 790–826

[24] Nishida T. Global solutions for an initial-boundary value problem of a quasilinear hyperbolic systems. Proc Japan Acad, 1968, 44: 642–646

[25] Nishida T. Nonlinear hyperbolic equations and relates topics in fluid dynamics. Publ Math D´Orsay, 1978: 46–53

[26] Pan R H. Boundary effects and large time behavior for the system of compressible adiabatic flow through porous media. Michigan Math J, 2001, 49: 519–539

[27] Pan R H, Zhao K. The 3D compressible Euler equations with damping in a bounded domain. J Differ Equations, 2009, 246: 581–596

[28] Schochet S. The compressible Euler equations in a bounded domain: Existence of solutions and the incom-
pressible limit. Comm Math Phys, 1986, 104: 49–75

[29] Sideris T C, Thomases B, Wang D H. Long time behavior of solutions to the 3D compressible Euler equations with damping. Comm Partial Differential Equations, 2003, 28: 795–816

[30] Tan Z, Wu G C. Large time behavior of solutions for compressible Euler equations with damping in R3. J Differ Equations, 2012, 252(2): 1546–1561

[31] Tan Z, Wang H Q. Global existence and optimal decay rate for the strong solutions in H2 to the 3-D compressible Navier-Stokes equations without heat conductivity. J Math Anal Appl, 2012, 394(2): 571–580

[32] Wang W, Yang T. The pointwise estimates of solutions for Euler equations with damping in multi-dimensions. J Differ Equations, 2001, 173: 410–450

[33] Zhang Y H, Tan Z. Existence and asymptotic behavior of global smooth solution for p-system with damping and boundary effect. Nonlinear Anal, 2010, 72(5): 2499–2513

[34] Zhao H J. Convergence to strong nonlinear diffusion waves for solutions of p-system with damping. J Differ
Equations, 2001, 174: 200–236

[35] Zheng Y. Global smooth solutions to the adiabatic gas dynamics system with dissipation terms. Chinese Ann Math, 1996, 17A: 155–162

[36] Zhu C J. Convergence rates to nonlinear diffusion waves for weak entropy solutions to p-system with damping. Sci China, Ser A, 2003, 46: 562–575

[37] Zhu C J, Jiang M N. Lp-decay rates to nonlinear diffusion waves for p-system with nonlinear damping. Sci China, Ser A, 2006, 49(6): 721–739