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Best asymptotic profile for the system of compressible adiabatic flow through porous media on quadrant
1. | School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China |
2. | Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, China |
References:
[1] |
S. Geng and Z. Wang, Convergence rates to nonlinear diffusion waves for solutions to the system of compressible adiabatic flow through porous media, Comm. Partial Differential Equations, 36 (2011), 850-872.
doi: 10.1080/03605302.2010.520052. |
[2] |
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. |
[3] |
L. Hsiao and T. Luo, Nonlinear diffusive phenomena of solutions for the system of compressible adiabatic flow through porous media, J. Differential Equations, 125 (1996), 329-365.
doi: 10.1006/jdeq.1996.0034. |
[4] |
L. Hsiao and D. Serre, Large-time behavior of solutions for the system of compressible adiabatic flow through porous media, Chinese Ann. Math. Ser. B, 16 (1995), 431-444. |
[5] |
L. Hsiao and D. Serre, Global existence of solutions for the system of compressible adiabatic flow through porous media, SIAM J. Math. Anal., 27 (1996), 70-77.
doi: 10.1137/S0036141094267078. |
[6] |
H. Ma and M. Mei, Best asymptotic profile for linear damped $p$-system with boundary effect, J. Differential Equations, 249 (2010), 446-484.
doi: 10.1016/j.jde.2010.04.008. |
[7] |
P. Marcati, M. Mei and B. Rubino, Optimal convergence rates to diffusion waves for solutions of the hyperbolic conservation laws with damping, J. Math. Fluid Mech., 7 (2005), S224-S240.
doi: 10.1007/s00021-005-0155-9. |
[8] |
P. Marcati and K. Nishihara, The $L^p$-$L^q$ estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media, J. Differential Equations, 191 (2003), 445-469.
doi: 10.1016/S0022-0396(03)00026-3. |
[9] |
P. Marcati and R. Pan, On the diffusive profiles for the system of compressible adiabatic flow through porous media, SIAM J. Math. Anal., 33 (2001), 790-826.
doi: 10.1137/S0036141099364401. |
[10] |
A. Matsumura, Global existence and asymptotics of the solutions of the second-order quasilinear hyperbolic equations with the first-order dissipation,, Publ. Res. Inst. Math. Sci., 13 (): 349.
doi: 10.2977/prims/1195189813. |
[11] |
M. Mei, Best asymptotic profile for hyperbolic $p$-system with damping, SIAM J. Math. Anal., 42 (2010), 1-23.
doi: 10.1137/090756594. |
[12] |
K. Nishihara, Convergence rates to nonlinear diffusion waves for solutions of system of hyperbolic conservation laws with damping, J. Differential Equations, 131 (1996), 171-188.
doi: 10.1006/jdeq.1996.0159. |
[13] |
K. Nishihara, Asymptotics toward the diffusion wave for a one-dimensional compressible flow through porous media, Proc. Roy. Soc. Edinburgh Sect. A, 133 (2003), 177-196.
doi: 10.1017/S0308210500002341. |
[14] |
K. Nishihara and M. Nishikawa, Asymptotic behavior of solutions to the system of compressible adiabatic flow through porous media, SIAM J. Math. Anal., 33 (2001), 216-239.
doi: 10.1137/S003614109936467X. |
[15] |
K. Nishihara, W. Wang and T. Yang, $L^p$-convergence rate to nonlinear diffusion waves for $p$-system with damping, J. Differential Equations, 161 (2000), 191-218.
doi: 10.1006/jdeq.1999.3703. |
[16] |
R. Pan, Boundary effects and large time behavior for the system of compressible adiabatic flow through porous media, Michigan Math. J., 49 (2001), 519-540.
doi: 10.1307/mmj/1012409969. |
[17] |
R. Pan, Darcy's law as long-time limit of adiabatic porous media flow, J. Differential Equations, 220 (2006), 121-146.
doi: 10.1016/j.jde.2004.10.013. |
[18] |
B. Said-Houari, Convergence to strong nonlinear diffusion waves for solutions to $p$-system with damping, J. Differential Equations, 247 (2009), 917-930.
doi: 10.1016/j.jde.2009.04.011. |
[19] |
H. Zhao, Convergence to strong nonlinear diffusion waves for solutions of $p$-system with damping, J. Differential Equations, 174 (2001), 200-236.
doi: 10.1006/jdeq.2000.3936. |
[20] |
C. 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: 10.1007/BF02884028. |
show all references
References:
[1] |
S. Geng and Z. Wang, Convergence rates to nonlinear diffusion waves for solutions to the system of compressible adiabatic flow through porous media, Comm. Partial Differential Equations, 36 (2011), 850-872.
doi: 10.1080/03605302.2010.520052. |
[2] |
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. |
[3] |
L. Hsiao and T. Luo, Nonlinear diffusive phenomena of solutions for the system of compressible adiabatic flow through porous media, J. Differential Equations, 125 (1996), 329-365.
doi: 10.1006/jdeq.1996.0034. |
[4] |
L. Hsiao and D. Serre, Large-time behavior of solutions for the system of compressible adiabatic flow through porous media, Chinese Ann. Math. Ser. B, 16 (1995), 431-444. |
[5] |
L. Hsiao and D. Serre, Global existence of solutions for the system of compressible adiabatic flow through porous media, SIAM J. Math. Anal., 27 (1996), 70-77.
doi: 10.1137/S0036141094267078. |
[6] |
H. Ma and M. Mei, Best asymptotic profile for linear damped $p$-system with boundary effect, J. Differential Equations, 249 (2010), 446-484.
doi: 10.1016/j.jde.2010.04.008. |
[7] |
P. Marcati, M. Mei and B. Rubino, Optimal convergence rates to diffusion waves for solutions of the hyperbolic conservation laws with damping, J. Math. Fluid Mech., 7 (2005), S224-S240.
doi: 10.1007/s00021-005-0155-9. |
[8] |
P. Marcati and K. Nishihara, The $L^p$-$L^q$ estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media, J. Differential Equations, 191 (2003), 445-469.
doi: 10.1016/S0022-0396(03)00026-3. |
[9] |
P. Marcati and R. Pan, On the diffusive profiles for the system of compressible adiabatic flow through porous media, SIAM J. Math. Anal., 33 (2001), 790-826.
doi: 10.1137/S0036141099364401. |
[10] |
A. Matsumura, Global existence and asymptotics of the solutions of the second-order quasilinear hyperbolic equations with the first-order dissipation,, Publ. Res. Inst. Math. Sci., 13 (): 349.
doi: 10.2977/prims/1195189813. |
[11] |
M. Mei, Best asymptotic profile for hyperbolic $p$-system with damping, SIAM J. Math. Anal., 42 (2010), 1-23.
doi: 10.1137/090756594. |
[12] |
K. Nishihara, Convergence rates to nonlinear diffusion waves for solutions of system of hyperbolic conservation laws with damping, J. Differential Equations, 131 (1996), 171-188.
doi: 10.1006/jdeq.1996.0159. |
[13] |
K. Nishihara, Asymptotics toward the diffusion wave for a one-dimensional compressible flow through porous media, Proc. Roy. Soc. Edinburgh Sect. A, 133 (2003), 177-196.
doi: 10.1017/S0308210500002341. |
[14] |
K. Nishihara and M. Nishikawa, Asymptotic behavior of solutions to the system of compressible adiabatic flow through porous media, SIAM J. Math. Anal., 33 (2001), 216-239.
doi: 10.1137/S003614109936467X. |
[15] |
K. Nishihara, W. Wang and T. Yang, $L^p$-convergence rate to nonlinear diffusion waves for $p$-system with damping, J. Differential Equations, 161 (2000), 191-218.
doi: 10.1006/jdeq.1999.3703. |
[16] |
R. Pan, Boundary effects and large time behavior for the system of compressible adiabatic flow through porous media, Michigan Math. J., 49 (2001), 519-540.
doi: 10.1307/mmj/1012409969. |
[17] |
R. Pan, Darcy's law as long-time limit of adiabatic porous media flow, J. Differential Equations, 220 (2006), 121-146.
doi: 10.1016/j.jde.2004.10.013. |
[18] |
B. Said-Houari, Convergence to strong nonlinear diffusion waves for solutions to $p$-system with damping, J. Differential Equations, 247 (2009), 917-930.
doi: 10.1016/j.jde.2009.04.011. |
[19] |
H. Zhao, Convergence to strong nonlinear diffusion waves for solutions of $p$-system with damping, J. Differential Equations, 174 (2001), 200-236.
doi: 10.1006/jdeq.2000.3936. |
[20] |
C. 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: 10.1007/BF02884028. |
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