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Nonlinear stability of Broadwell model with Maxwell diffuse boundary condition
Energy estimate for a linear symmetric hyperbolic-parabolic system in half line
1. | Faculty of Mathematics, Kyushu University, Fukuoka 819-0395, Japan |
2. | Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552 |
References:
[1] |
Y. Kagei and S. Kawashima, Local solvability of an initial boundary value problem for a quasilinear hyperbolic-parabolic system,, J. Hyperbolic Differ. Equ., 3 (2006), 195.
doi: 10.1142/S0219891606000768. |
[2] |
T. Kato, Linear evolution equations of hyperbolic type, II,, J. Math. Soc. Japan, 25 (1973), 648.
doi: 10.2969/jmsj/02540648. |
[3] |
S. Kawashima, Systems of A Hyperbolic-Parabolic Composite Type, with Applications to the Equations of Magnetohydrodynamics,, Doctoral Thesis, (1984). Google Scholar |
[4] |
S. Kawashima, Large-time behaviour of solutions to hyperbolic-parabolic systems of conservation laws and applications,, Proc. Roy. Soc. Edinburgh, 106 (1987), 169.
doi: 10.1017/S0308210500018308. |
[5] |
S. Kawashima, T. Nakamura, S. Nishibata and P. Zhu, Stationary waves to viscous heat-conductive gases in half-space: existence, stability and convergence rate,, Math. Models Methods Appl. Sci., 20 (2010), 2201.
doi: 10.1142/S0218202510004908. |
[6] |
S. Kawashima, S. Nishibata and P. Zhu, Asymptotic stability of the stationary solution to the compressible Navier-Stokes equations in the half space,, Comm. Math. Phys., 240 (2003), 483.
|
[7] |
B. Kwon, M. Suzuki and M. Takayama, Large-time behavior of solutions to an outflow problem for a shallow water model,, J. Differential Equations, 255 (2013), 1883.
doi: 10.1016/j.jde.2013.05.025. |
[8] |
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.
|
[9] |
A. Matsumura and T. Nishida, Initial-boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids,, Comm. Math. Phys., 89 (1983), 445.
doi: 10.1007/BF01214738. |
[10] |
A. Matsumura and K. Nishihara, Large-time behaviors of solutions to an inflow problem in the half space for a one-dimensional system of compressible viscous gas,, Comm. Math. Phys., 222 (2001), 449.
doi: 10.1007/s002200100517. |
[11] |
T. Nakamura and S. Nishibata, Stationary waves for symmetric hyperbolic-parabolic systems in half line and application to fluid dynamics,, preprint., (). Google Scholar |
[12] |
T. Nakamura and S. Nishibata, Convergence rate toward planar stationary waves for compressible viscous fluid in multi-dimensional half space,, SIAM J. Math. Anal., 41 (2009), 1757.
doi: 10.1137/090755357. |
[13] |
T. Nakamura and S. Nishibata, Stationary wave associated with an inflow problem in the half line for viscous heat-conductive gas,, J. Hyperbolic Differ. Equ., 8 (2011), 651.
doi: 10.1142/S0219891611002524. |
[14] |
T. Nakamura, S. Nishibata and T. Yuge, Convergence rate of solutions toward stationary solutions to the compressible Navier-Stokes equation in a half line,, J. Differential Equations, 241 (2007), 94.
doi: 10.1016/j.jde.2007.06.016. |
[15] |
Y. Shizuta and S. Kawashima, Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation,, Hokkaido Math. J., 14 (1985), 249.
|
[16] |
T. Umeda, S. Kawashima and Y. Shizuta, On the decay of solutions to the linearized equations of electromagnetofluid dynamics,, Japan J. Appl. Math., 1 (1984), 435.
doi: 10.1007/BF03167068. |
show all references
References:
[1] |
Y. Kagei and S. Kawashima, Local solvability of an initial boundary value problem for a quasilinear hyperbolic-parabolic system,, J. Hyperbolic Differ. Equ., 3 (2006), 195.
doi: 10.1142/S0219891606000768. |
[2] |
T. Kato, Linear evolution equations of hyperbolic type, II,, J. Math. Soc. Japan, 25 (1973), 648.
doi: 10.2969/jmsj/02540648. |
[3] |
S. Kawashima, Systems of A Hyperbolic-Parabolic Composite Type, with Applications to the Equations of Magnetohydrodynamics,, Doctoral Thesis, (1984). Google Scholar |
[4] |
S. Kawashima, Large-time behaviour of solutions to hyperbolic-parabolic systems of conservation laws and applications,, Proc. Roy. Soc. Edinburgh, 106 (1987), 169.
doi: 10.1017/S0308210500018308. |
[5] |
S. Kawashima, T. Nakamura, S. Nishibata and P. Zhu, Stationary waves to viscous heat-conductive gases in half-space: existence, stability and convergence rate,, Math. Models Methods Appl. Sci., 20 (2010), 2201.
doi: 10.1142/S0218202510004908. |
[6] |
S. Kawashima, S. Nishibata and P. Zhu, Asymptotic stability of the stationary solution to the compressible Navier-Stokes equations in the half space,, Comm. Math. Phys., 240 (2003), 483.
|
[7] |
B. Kwon, M. Suzuki and M. Takayama, Large-time behavior of solutions to an outflow problem for a shallow water model,, J. Differential Equations, 255 (2013), 1883.
doi: 10.1016/j.jde.2013.05.025. |
[8] |
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.
|
[9] |
A. Matsumura and T. Nishida, Initial-boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids,, Comm. Math. Phys., 89 (1983), 445.
doi: 10.1007/BF01214738. |
[10] |
A. Matsumura and K. Nishihara, Large-time behaviors of solutions to an inflow problem in the half space for a one-dimensional system of compressible viscous gas,, Comm. Math. Phys., 222 (2001), 449.
doi: 10.1007/s002200100517. |
[11] |
T. Nakamura and S. Nishibata, Stationary waves for symmetric hyperbolic-parabolic systems in half line and application to fluid dynamics,, preprint., (). Google Scholar |
[12] |
T. Nakamura and S. Nishibata, Convergence rate toward planar stationary waves for compressible viscous fluid in multi-dimensional half space,, SIAM J. Math. Anal., 41 (2009), 1757.
doi: 10.1137/090755357. |
[13] |
T. Nakamura and S. Nishibata, Stationary wave associated with an inflow problem in the half line for viscous heat-conductive gas,, J. Hyperbolic Differ. Equ., 8 (2011), 651.
doi: 10.1142/S0219891611002524. |
[14] |
T. Nakamura, S. Nishibata and T. Yuge, Convergence rate of solutions toward stationary solutions to the compressible Navier-Stokes equation in a half line,, J. Differential Equations, 241 (2007), 94.
doi: 10.1016/j.jde.2007.06.016. |
[15] |
Y. Shizuta and S. Kawashima, Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation,, Hokkaido Math. J., 14 (1985), 249.
|
[16] |
T. Umeda, S. Kawashima and Y. Shizuta, On the decay of solutions to the linearized equations of electromagnetofluid dynamics,, Japan J. Appl. Math., 1 (1984), 435.
doi: 10.1007/BF03167068. |
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