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Seiji Ukai
A Milne problem from a Bose condensate with excitations
1. | Mathematical Sciences, 41296 Göteborg, Sweden |
2. | LATP, Aix-Marseille University, France |
References:
[1] |
L. Arkeryd and A. Nouri, Bose condensates in interaction with excitations - a kinetic model,, Commun. Math. Phys., 310 (2012), 765.
doi: 10.1007/s00220-012-1415-1. |
[2] |
L. Arkeryd and A. Nouri, Bose Condensates in Interaction with Excitations - A Two-Component, Space Dependent Model Close to Equilibrium,, in preparation., (). Google Scholar |
[3] |
L. Arkeryd and A. Nouri, On the Milne problem and the hydrodynamic limit for a steady Boltzmann equation model,, J. Stat. Phys., 99 (2000), 993.
doi: 10.1023/A:1018655815285. |
[4] |
A. V. Bobylev and N. Bernhoff, Discrete velocity models and dynamic systems,, in Lecture Notes on the discretization of the Boltzmann equation (eds. World Sci. Pub. I), 63 (2003), 203.
doi: 10.1142/9789812796905_0008. |
[5] |
C. Bardos, R. E. Caflish and B. Nicolaenko, The Milne and Kramers problems for the Boltzmann equation of a hard sphere gas,, Commun. Pure Appl. Math., 39 (1986), 323.
doi: 10.1002/cpa.3160390304. |
[6] |
C. Bardos, F. Golse and Y. Sone, Half-space problems for the Boltzmann equation: A survey,, J. Stat. Phys., 124 (2006), 275.
doi: 10.1007/s10955-006-9077-z. |
[7] |
A. V. Bobylev and G. Toscani, Two-dimensional half space problems for the Broadwell discrete velocity model,, Contin. Mech. Thermodyn., 8 (1996), 257.
doi: 10.1007/s001610050043. |
[8] |
C. Cercignani, Half-space problems in the kinetic theory of gases,, Trends in applications of pure mathematics to mechanics (Bad Honnef, 249 (1986), 35.
doi: 10.1007/BFb0016381. |
[9] |
F. Coron, F. Golse and C. Sulem, A classification of well-posed kinetic layer problems,, Commun. Pure Appl. Math., 41 (1988), 409.
doi: 10.1002/cpa.3160410403. |
[10] |
C. Cercignani, R. Marra and R. Esposito, The Milne problem with a force term,, Transport Theory and Statistical Physics, 27 (1998), 1.
doi: 10.1080/00411459808205139. |
[11] |
F. Golse and F. Poupaud, Stationary solutions of the linearized Boltzmann equation in a half-space,, Math. Methods Appl. Sci., 11 (1989), 483.
doi: 10.1002/mma.1670110406. |
[12] |
N. Maslova, The Kramers problems in the kinetic theory of gases,, USSR Comput. Math. Phys., 22 (1982), 208. Google Scholar |
[13] |
N. Maslova, Nonlinear Evolution Equations,, Kinetic approach. Series on Advances in Mathematics for Applied Sciences, (1993).
|
[14] |
F. Poupaud, Diffusion approximation of the linear semiconductor equation: analysis of boundary layers,, Asymptotic Analysis, 4 (1991), 293.
|
[15] |
Y. Sone, Kinetic Theory and Fluid Dynamics,, Birkhauser Boston, (2002). Google Scholar |
[16] |
Y. Sone, Molecular Gas Dynamics,, Theory, (2007).
doi: 10.1007/978-0-8176-4573-1. |
[17] |
S. Ukai, T. Yang and S.-H. Yu, Nonlinear boundary layers of the Boltzmann equation: I. Existence,, Commun. Math. Phys., 236 (2003), 373.
doi: 10.1007/s00220-003-0822-8. |
[18] |
S. Ukai, T. Yang and S.-H. Yu, Nonlinear stability of boundary layers of the Boltzmann equation; I. The case $\mathcalM_\infty <-1$,, Commun. Math. Phys., 244 (2004), 99.
doi: 10.1007/s00220-003-0976-4. |
show all references
References:
[1] |
L. Arkeryd and A. Nouri, Bose condensates in interaction with excitations - a kinetic model,, Commun. Math. Phys., 310 (2012), 765.
doi: 10.1007/s00220-012-1415-1. |
[2] |
L. Arkeryd and A. Nouri, Bose Condensates in Interaction with Excitations - A Two-Component, Space Dependent Model Close to Equilibrium,, in preparation., (). Google Scholar |
[3] |
L. Arkeryd and A. Nouri, On the Milne problem and the hydrodynamic limit for a steady Boltzmann equation model,, J. Stat. Phys., 99 (2000), 993.
doi: 10.1023/A:1018655815285. |
[4] |
A. V. Bobylev and N. Bernhoff, Discrete velocity models and dynamic systems,, in Lecture Notes on the discretization of the Boltzmann equation (eds. World Sci. Pub. I), 63 (2003), 203.
doi: 10.1142/9789812796905_0008. |
[5] |
C. Bardos, R. E. Caflish and B. Nicolaenko, The Milne and Kramers problems for the Boltzmann equation of a hard sphere gas,, Commun. Pure Appl. Math., 39 (1986), 323.
doi: 10.1002/cpa.3160390304. |
[6] |
C. Bardos, F. Golse and Y. Sone, Half-space problems for the Boltzmann equation: A survey,, J. Stat. Phys., 124 (2006), 275.
doi: 10.1007/s10955-006-9077-z. |
[7] |
A. V. Bobylev and G. Toscani, Two-dimensional half space problems for the Broadwell discrete velocity model,, Contin. Mech. Thermodyn., 8 (1996), 257.
doi: 10.1007/s001610050043. |
[8] |
C. Cercignani, Half-space problems in the kinetic theory of gases,, Trends in applications of pure mathematics to mechanics (Bad Honnef, 249 (1986), 35.
doi: 10.1007/BFb0016381. |
[9] |
F. Coron, F. Golse and C. Sulem, A classification of well-posed kinetic layer problems,, Commun. Pure Appl. Math., 41 (1988), 409.
doi: 10.1002/cpa.3160410403. |
[10] |
C. Cercignani, R. Marra and R. Esposito, The Milne problem with a force term,, Transport Theory and Statistical Physics, 27 (1998), 1.
doi: 10.1080/00411459808205139. |
[11] |
F. Golse and F. Poupaud, Stationary solutions of the linearized Boltzmann equation in a half-space,, Math. Methods Appl. Sci., 11 (1989), 483.
doi: 10.1002/mma.1670110406. |
[12] |
N. Maslova, The Kramers problems in the kinetic theory of gases,, USSR Comput. Math. Phys., 22 (1982), 208. Google Scholar |
[13] |
N. Maslova, Nonlinear Evolution Equations,, Kinetic approach. Series on Advances in Mathematics for Applied Sciences, (1993).
|
[14] |
F. Poupaud, Diffusion approximation of the linear semiconductor equation: analysis of boundary layers,, Asymptotic Analysis, 4 (1991), 293.
|
[15] |
Y. Sone, Kinetic Theory and Fluid Dynamics,, Birkhauser Boston, (2002). Google Scholar |
[16] |
Y. Sone, Molecular Gas Dynamics,, Theory, (2007).
doi: 10.1007/978-0-8176-4573-1. |
[17] |
S. Ukai, T. Yang and S.-H. Yu, Nonlinear boundary layers of the Boltzmann equation: I. Existence,, Commun. Math. Phys., 236 (2003), 373.
doi: 10.1007/s00220-003-0822-8. |
[18] |
S. Ukai, T. Yang and S.-H. Yu, Nonlinear stability of boundary layers of the Boltzmann equation; I. The case $\mathcalM_\infty <-1$,, Commun. Math. Phys., 244 (2004), 99.
doi: 10.1007/s00220-003-0976-4. |
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