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Stability of a Vlasov-Boltzmann binary mixture at the phase transition on an interval
1. | International Research Center M&MOCS, Università di L'Aquila, Cisterna di Latina, 04012, Italy |
2. | Division of Applied Mathematics, Brown University, Providence, RI 02812 |
3. | Dipartimento di Fisica and Unità INFN, Università di Roma Tor Vergata, 00133 Roma |
References:
[1] |
S. Bastea, R. Esposito, J. L. Lebowitz and R. Marra, Binary fluids with long range segregating interaction I: Derivation of kinetic and hydrodynamic equation, J. Statist. Phys, 101 (2000), 1087-1136.
doi: 10.1023/A:1026481706240. |
[2] |
S. Bastea and J. L. Lebowitz, Spinodal decomposition in binary gases, Phys. Rev. Lett., 78 (1997), 3499-3502.
doi: 10.1103/PhysRevLett.78.3499. |
[3] |
E. A. Carlen, M. Carvalho, R. Esposito, J. L. Lebowitz and R. Marra, Free energy minimizers for a two-species model with segregation and liquid-vapor transition, Nonlinearity, 16 (2003), 1075-1105.
doi: 10.1088/0951-7715/16/3/316. |
[4] |
E. A. Carlen, M. C. Carvalho, R. Esposito, J. L. Lebowitz and R. Marra, Displacement convexity and minimal fronts at phase boundaries, Arch. Rat. Mech. Anal., 194 (2009), 823-847.
doi: 10.1007/s00205-008-0190-9. |
[5] |
A. De Masi, E. Olivieri and E. Presutti, Spectral properties of integral operators in problems of interface dynamics and metastability, Markov Processes and Related Fields, 4 (1998), 27-112. |
[6] |
R. Esposito , Y. Guo and R. Marra, Stability of the front under a Vlasov-Fokker-Planck dynamics, Arch. Rational Mech. Anal., 195 (2010), 75-116.
doi: 10.1007/s00205-008-0184-7. |
[7] |
R. Esposito, Y. Guo and R. Marra, Phase transition in a Vlasov-Boltzmann binary mixture, Commun. Math. Phys., 296 (2010), 1-33.
doi: 10.1007/s00220-010-1009-8. |
[8] |
Yan Guo, Decay and continuity of the Boltzmann equation in bounded domains, Arch. Rational Mech. Anal., 197 (2010), 713-809.
doi: 10.1007/s00205-009-0285-y. |
[9] |
Y. Guo and W. A. Strauss, Unstable oscillatory-tail waves in collisionless plasmas, SIAM J. Math. Anal., 30 (1999), 1076-1114 (electronic).
doi: 10.1137/S0036131098333918. |
[10] |
T. Kato, Perturbation Theory for Linear Operators, Second edition. Grundlehren der Mathematischen Wissenschaften, Band 132. Springer-Verlag, Berlin-New York, 1976. |
[11] |
O. Penrose, Electrostatic instability of a non-Maxwellian plasma, Phys. Fluids., 3 (1960), 258-265.
doi: 10.1063/1.1706024. |
[12] |
E. Presutti, Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics, Theoretical and Mathematical Physics. Springer, Berlin, 2009. |
show all references
References:
[1] |
S. Bastea, R. Esposito, J. L. Lebowitz and R. Marra, Binary fluids with long range segregating interaction I: Derivation of kinetic and hydrodynamic equation, J. Statist. Phys, 101 (2000), 1087-1136.
doi: 10.1023/A:1026481706240. |
[2] |
S. Bastea and J. L. Lebowitz, Spinodal decomposition in binary gases, Phys. Rev. Lett., 78 (1997), 3499-3502.
doi: 10.1103/PhysRevLett.78.3499. |
[3] |
E. A. Carlen, M. Carvalho, R. Esposito, J. L. Lebowitz and R. Marra, Free energy minimizers for a two-species model with segregation and liquid-vapor transition, Nonlinearity, 16 (2003), 1075-1105.
doi: 10.1088/0951-7715/16/3/316. |
[4] |
E. A. Carlen, M. C. Carvalho, R. Esposito, J. L. Lebowitz and R. Marra, Displacement convexity and minimal fronts at phase boundaries, Arch. Rat. Mech. Anal., 194 (2009), 823-847.
doi: 10.1007/s00205-008-0190-9. |
[5] |
A. De Masi, E. Olivieri and E. Presutti, Spectral properties of integral operators in problems of interface dynamics and metastability, Markov Processes and Related Fields, 4 (1998), 27-112. |
[6] |
R. Esposito , Y. Guo and R. Marra, Stability of the front under a Vlasov-Fokker-Planck dynamics, Arch. Rational Mech. Anal., 195 (2010), 75-116.
doi: 10.1007/s00205-008-0184-7. |
[7] |
R. Esposito, Y. Guo and R. Marra, Phase transition in a Vlasov-Boltzmann binary mixture, Commun. Math. Phys., 296 (2010), 1-33.
doi: 10.1007/s00220-010-1009-8. |
[8] |
Yan Guo, Decay and continuity of the Boltzmann equation in bounded domains, Arch. Rational Mech. Anal., 197 (2010), 713-809.
doi: 10.1007/s00205-009-0285-y. |
[9] |
Y. Guo and W. A. Strauss, Unstable oscillatory-tail waves in collisionless plasmas, SIAM J. Math. Anal., 30 (1999), 1076-1114 (electronic).
doi: 10.1137/S0036131098333918. |
[10] |
T. Kato, Perturbation Theory for Linear Operators, Second edition. Grundlehren der Mathematischen Wissenschaften, Band 132. Springer-Verlag, Berlin-New York, 1976. |
[11] |
O. Penrose, Electrostatic instability of a non-Maxwellian plasma, Phys. Fluids., 3 (1960), 258-265.
doi: 10.1063/1.1706024. |
[12] |
E. Presutti, Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics, Theoretical and Mathematical Physics. Springer, Berlin, 2009. |
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