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Nonlinear stability of Broadwell model with Maxwell diffuse boundary condition
1. | Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China |
2. | Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, 119076, Singapore, Singapore |
References:
[1] |
R.-E. Caflisch and T.-P. Liu, Stability of shock waves for the Broadwell equations, Comm. Math. Phys., 114 (1988), 103-130.
doi: 10.1007/BF01218291. |
[2] |
R.-E. Caflisch, Navier-Stokes and Boltzmann shock profiles for a model of gas dynamics, Comm. Pure. Appl. Math, 32 (1979), 521-554.
doi: 10.1002/cpa.3160320404. |
[3] |
S.-J. Deng, W.-K. Wang and S.-H. Yu, Pointwise convergence to a Maxwellian for a Broadwell model with a supersonic boundary, Netw. Heterog. Media, 2 (2007), 383-395.
doi: 10.3934/nhm.2007.2.383. |
[4] |
S.-J. Deng, W.-K. Wang and S.-H. Yu, Broadwell model and conservative supersonic boundary, Arch. Ration. Mech. Anal., 200 (2011), 203-223.
doi: 10.1007/s00205-010-0344-4. |
[5] |
S.-J. Deng, W.-K. Wang and S.-H. Yu, Bifurcation on Boundary Data for Linear Broadwell Model with Conservative Boundary Condition,, to appear., ().
|
[6] |
C.-Y. Lan, H.-E. Lin and S.-H. Yu, The Green's functions for the Broadwell model in a half space problem, Netw. Heterog. Media, 1 (2006), 167-183.
doi: 10.3934/nhm.2006.1.167. |
[7] |
H.-E. Lin, Nonlinear stability of the initial-boundary value problem for the Broadwell model around a Maxwellian, J. Hyperbolic Differ. Equ., 8 (2011), 131-157.
doi: 10.1142/S0219891611002354. |
[8] |
J.-G. Liu and Z.-P. Xin, Boundary-layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation, Arch. Rational Mech. Anal., 135 (1996), 61-105.
doi: 10.1007/BF02198435. |
[9] |
T.-P. Liu, Pointwise convergence to shock waves for viscous conservarion laws, Commun. Pure Appl. Math., 50 (1997), 1113-1182.
doi: 10.1002/(SICI)1097-0312(199711)50:11<1113::AID-CPA3>3.0.CO;2-D. |
[10] |
T.-P. Liu and S.-H. Yu, Boltzmann equation: micro-macro decompostions and positivity of shock profiles, Comm. Math. Phys., 246 (2004), 133-179.
doi: 10.1007/s00220-003-1030-2. |
[11] |
T.-P. Liu and S.-H. Yu, Initial-boundary value problem for one-dimensional wave solutions of the Boltzmann equation, Commun. Pure Appl. Math., 60 (2007), 295-356.
doi: 10.1002/cpa.20172. |
[12] |
T.-P. Liu and S.-H. Yu, On boundary relation for some dissipative systems, Bull. Inst. Math. Acad. Sin. (N.S.), 6 (2011), 245-267. |
[13] |
T.-P. Liu and S.-H. Yu, Dirichlet-Neumann kernel for dissipative system in half-space, Bull. Inst. Math. Acad. Sin. (N.S.), 7 (2012), 477-543. |
[14] |
M. Slemrod and A.-E. Tzavaras, Self-similiar fluid-dynamic limits for the Broadwell system, Arch. Ration. Mech. Anal., 122 (1993), 353-392.
doi: 10.1007/BF00375140. |
[15] |
M. Slemrod, Large time behavior of the Broadwell model of a discrete velocity gas with specularly reflective boundary conditions, Arch. Ration. Mech. Anal., 111 (1990), 323-342.
doi: 10.1007/BF00376025. |
[16] |
Y. Sone, Kinetic Theory and Fluid Dynamics, Modeling and Simulation in Science, Engineering and Technology. Birkhäuster Boston, Inc., Boston, MA, 2002.
doi: 10.1007/978-1-4612-0061-1. |
[17] |
Y. Sone, Molecular Gas Dynamics: Theory, Techniques, and Applications, Modeling and Simulation in Science, Engineering and Technology. Birkhäuster Boston, Inc., Boston, MA, 2007.
doi: 10.1007/978-0-8176-4573-1. |
[18] |
Z.-P. Xin, The fluid-dynamic limit of the Broadwell model of the nonlinear Boltzmann equation in the presence of shocks, Comm. Pure Appl. Math, 44 (1991), 679-713.
doi: 10.1002/cpa.3160440604. |
show all references
References:
[1] |
R.-E. Caflisch and T.-P. Liu, Stability of shock waves for the Broadwell equations, Comm. Math. Phys., 114 (1988), 103-130.
doi: 10.1007/BF01218291. |
[2] |
R.-E. Caflisch, Navier-Stokes and Boltzmann shock profiles for a model of gas dynamics, Comm. Pure. Appl. Math, 32 (1979), 521-554.
doi: 10.1002/cpa.3160320404. |
[3] |
S.-J. Deng, W.-K. Wang and S.-H. Yu, Pointwise convergence to a Maxwellian for a Broadwell model with a supersonic boundary, Netw. Heterog. Media, 2 (2007), 383-395.
doi: 10.3934/nhm.2007.2.383. |
[4] |
S.-J. Deng, W.-K. Wang and S.-H. Yu, Broadwell model and conservative supersonic boundary, Arch. Ration. Mech. Anal., 200 (2011), 203-223.
doi: 10.1007/s00205-010-0344-4. |
[5] |
S.-J. Deng, W.-K. Wang and S.-H. Yu, Bifurcation on Boundary Data for Linear Broadwell Model with Conservative Boundary Condition,, to appear., ().
|
[6] |
C.-Y. Lan, H.-E. Lin and S.-H. Yu, The Green's functions for the Broadwell model in a half space problem, Netw. Heterog. Media, 1 (2006), 167-183.
doi: 10.3934/nhm.2006.1.167. |
[7] |
H.-E. Lin, Nonlinear stability of the initial-boundary value problem for the Broadwell model around a Maxwellian, J. Hyperbolic Differ. Equ., 8 (2011), 131-157.
doi: 10.1142/S0219891611002354. |
[8] |
J.-G. Liu and Z.-P. Xin, Boundary-layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation, Arch. Rational Mech. Anal., 135 (1996), 61-105.
doi: 10.1007/BF02198435. |
[9] |
T.-P. Liu, Pointwise convergence to shock waves for viscous conservarion laws, Commun. Pure Appl. Math., 50 (1997), 1113-1182.
doi: 10.1002/(SICI)1097-0312(199711)50:11<1113::AID-CPA3>3.0.CO;2-D. |
[10] |
T.-P. Liu and S.-H. Yu, Boltzmann equation: micro-macro decompostions and positivity of shock profiles, Comm. Math. Phys., 246 (2004), 133-179.
doi: 10.1007/s00220-003-1030-2. |
[11] |
T.-P. Liu and S.-H. Yu, Initial-boundary value problem for one-dimensional wave solutions of the Boltzmann equation, Commun. Pure Appl. Math., 60 (2007), 295-356.
doi: 10.1002/cpa.20172. |
[12] |
T.-P. Liu and S.-H. Yu, On boundary relation for some dissipative systems, Bull. Inst. Math. Acad. Sin. (N.S.), 6 (2011), 245-267. |
[13] |
T.-P. Liu and S.-H. Yu, Dirichlet-Neumann kernel for dissipative system in half-space, Bull. Inst. Math. Acad. Sin. (N.S.), 7 (2012), 477-543. |
[14] |
M. Slemrod and A.-E. Tzavaras, Self-similiar fluid-dynamic limits for the Broadwell system, Arch. Ration. Mech. Anal., 122 (1993), 353-392.
doi: 10.1007/BF00375140. |
[15] |
M. Slemrod, Large time behavior of the Broadwell model of a discrete velocity gas with specularly reflective boundary conditions, Arch. Ration. Mech. Anal., 111 (1990), 323-342.
doi: 10.1007/BF00376025. |
[16] |
Y. Sone, Kinetic Theory and Fluid Dynamics, Modeling and Simulation in Science, Engineering and Technology. Birkhäuster Boston, Inc., Boston, MA, 2002.
doi: 10.1007/978-1-4612-0061-1. |
[17] |
Y. Sone, Molecular Gas Dynamics: Theory, Techniques, and Applications, Modeling and Simulation in Science, Engineering and Technology. Birkhäuster Boston, Inc., Boston, MA, 2007.
doi: 10.1007/978-0-8176-4573-1. |
[18] |
Z.-P. Xin, The fluid-dynamic limit of the Broadwell model of the nonlinear Boltzmann equation in the presence of shocks, Comm. Pure Appl. Math, 44 (1991), 679-713.
doi: 10.1002/cpa.3160440604. |
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