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Global classical solutions close to equilibrium to the Vlasov-Fokker-Planck-Euler system
Kinetic approach to deflagration processes in a recombination reaction
1. | Dipartimento di Matematica, Università di Messina, Viale F. Stagno d'Alcontres 31 - 98166 Messina, Italy |
2. | Dipartimento di Matematica, Università di Parma, V.le G.P. Usberti 53/A, 43100 Parma |
3. | Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24 - 10129 Torino, Italy |
4. | Dipartimento di Matematica, Università di Parma, V.le G.P. Usberti 53/A, 43124 Parma |
References:
[1] |
M. Bisi, M. Groppi and G. Spiga, Flame structure from a kinetic model for chemical reactions, Kinetic and Related Models, 3 (2010), 17-34.
doi: 10.3934/krm.2010.3.17. |
[2] |
V. C. Boffi, V. Protopopescu and G. Spiga, On the equivalence between the probabilistic, kinetic, and scattering kernel formulations of the Boltzmann equation, Physica A, 164 (1990), 400-410.
doi: 10.1016/0378-4371(90)90203-5. |
[3] |
C. Cercignani, "The Boltzmann Equation and its Applications,'' Springer, New York, 1988. |
[4] |
C. Cercignani, "Rarefied Gas Dynamics. From Basic Concepts to Actual Calculations,'' University Press, Cambridge, 2000. |
[5] |
S. Chapman and T. G. Cowling, "The Mathematical Theory of Non-Uniform Gases,'' University Press, Cambridge, 1990. |
[6] |
R. M. Colombo and A. Corli, Sonic and kinetic phase transitions with applications to Chapman–Jouguet deflagrations, Math. Meth. Appl. Sci., 27 (2004), 843-864.
doi: 10.1002/mma.474. |
[7] |
S. R. De Groot and P. Mazur, "Non-Equilibrium Thermodynamics,'' North-Holland, Amsterdam, 1963. |
[8] |
W. Fickett and W. C. Davis, "Detonation, Theory and Experiment,'' Dover, New York, 1979. |
[9] |
V. Giovangigli, "Multicomponent Flow Modeling,'' Birkhäuser, Boston, 1999. |
[10] | |
[11] |
M. Groppi, A. Rossani and G. Spiga, Kinetic theory of a diatomic gas with reactions of dissociation and recombination through a transition state, J. Phys. A: Math. Gen., 33 (2000), 8819-8833.
doi: 10.1088/0305-4470/33/48/317. |
[12] |
D. Jacob, "Introduction to Atmosperic Chemistry,'' University Press, Princeton, 1999. |
[13] |
L. He, Analysis of compressibility effects on Darrieus-Landau instability of deflagration wave, Europhys. Lett., 49 (2000), 576-582.
doi: 10.1209/epl/i2000-00189-8. |
[14] |
L. Kagan, On the transition from deflagration to detonation in narrow channels, Math. Model. Nat. Phenom., 2 (2007), 40-55.
doi: 10.1051/mmnp:2008018. |
[15] |
A. K. Kapila, B. J. Matkowsky and A. van Harten, An asymptotic theory of deflagrations and detonations. I. The steady solutions, SIAM J. Appl. Math., 43 (1983), 491-519.
doi: 10.1137/0143032. |
[16] |
K. K. Kuo, "Principles of Combustion,'' Wiley, Hoboken (New Jersey), 2005. |
[17] |
S. B. Margolis and M. R. Baer, A singular-perturbation analysis of the burning-rate eigenvalue for a two-temperature model of deflagrations in confined porous energetic materials, SIAM J. Appl. Math., 62 (2001), 627-663.
doi: 10.1137/S0036139900377780. |
[18] |
J. Menkes, On the stability of a plane deflagration wave, Proc. Roy. Soc. London. Ser. A, 253 (1959), 380-389. |
[19] |
J. R. Mika and J. Banasiak, "Singularly Perturbed Evolution Equations with Applications to Kinetic Theory,'' World, Singapore, 1995. |
[20] |
I. Müller, Flame structure in ordinary and extended thermodynamics, in "Asymptotic Methods in Nonlinear Wave Phenomena'' (eds. T. Ruggeri and M. Sammartino), World, Singapore, (2007), 144-153.
doi: 10.1142/9789812708908_0013. |
[21] |
L. Pan and W. Sheng, The scalar Zeldovich-von Neumann-Doering combustion model (II) interactions of shock and deflagration, Nonlinear Analysis: Real World Applications, 10 (2009), 449-457.
doi: 10.1016/j.nonrwa.2007.10.006. |
[22] |
W. C. Sheng and D. C. Tan, Weak deflagration solutions to the simplest combustion model, Journal of Differential Equations, 107 (1994), 207-230.
doi: 10.1006/jdeq.1994.1009. |
[23] |
S. Takata and K. Aoki, Two-surface problems of a multicomponent mixture of vapors and non condensable gases in the continuum limit in the light of kinetic theory, Phys. Fluids, 11 (1999), 2743-2756.
doi: 10.1063/1.870133. |
[24] |
S. Takata, Kinetic theory analysis of the two-surface problem of a vapor-vapor mixture in the continuum limit, Phys. Fluids, 16 (2004), 2182-2198.
doi: 10.1063/1.1723464. |
[25] |
D. H. Wagner, Existence of deflagration waves: Connection to a degenerate critical point, in "Lecture Notes in Pure and Appl. Math.," 102, Dekker, New York, (1985), 187-197. |
[26] |
Y. Yoshizawa, Wave structures of chemically reacting gas by the kinetic theory of gases, in "Rarefied Gas Dynamics'' (ed. J.L. Potter), A.I.A.A., New York, (1977), 501-517. |
[27] |
P. Zhang and T. Zhang, The Riemann problem for scalar CJ-combustion model without convexity, Discrete and Cont. Dynamical Systems, 1 (1995), 195-206. |
show all references
References:
[1] |
M. Bisi, M. Groppi and G. Spiga, Flame structure from a kinetic model for chemical reactions, Kinetic and Related Models, 3 (2010), 17-34.
doi: 10.3934/krm.2010.3.17. |
[2] |
V. C. Boffi, V. Protopopescu and G. Spiga, On the equivalence between the probabilistic, kinetic, and scattering kernel formulations of the Boltzmann equation, Physica A, 164 (1990), 400-410.
doi: 10.1016/0378-4371(90)90203-5. |
[3] |
C. Cercignani, "The Boltzmann Equation and its Applications,'' Springer, New York, 1988. |
[4] |
C. Cercignani, "Rarefied Gas Dynamics. From Basic Concepts to Actual Calculations,'' University Press, Cambridge, 2000. |
[5] |
S. Chapman and T. G. Cowling, "The Mathematical Theory of Non-Uniform Gases,'' University Press, Cambridge, 1990. |
[6] |
R. M. Colombo and A. Corli, Sonic and kinetic phase transitions with applications to Chapman–Jouguet deflagrations, Math. Meth. Appl. Sci., 27 (2004), 843-864.
doi: 10.1002/mma.474. |
[7] |
S. R. De Groot and P. Mazur, "Non-Equilibrium Thermodynamics,'' North-Holland, Amsterdam, 1963. |
[8] |
W. Fickett and W. C. Davis, "Detonation, Theory and Experiment,'' Dover, New York, 1979. |
[9] |
V. Giovangigli, "Multicomponent Flow Modeling,'' Birkhäuser, Boston, 1999. |
[10] | |
[11] |
M. Groppi, A. Rossani and G. Spiga, Kinetic theory of a diatomic gas with reactions of dissociation and recombination through a transition state, J. Phys. A: Math. Gen., 33 (2000), 8819-8833.
doi: 10.1088/0305-4470/33/48/317. |
[12] |
D. Jacob, "Introduction to Atmosperic Chemistry,'' University Press, Princeton, 1999. |
[13] |
L. He, Analysis of compressibility effects on Darrieus-Landau instability of deflagration wave, Europhys. Lett., 49 (2000), 576-582.
doi: 10.1209/epl/i2000-00189-8. |
[14] |
L. Kagan, On the transition from deflagration to detonation in narrow channels, Math. Model. Nat. Phenom., 2 (2007), 40-55.
doi: 10.1051/mmnp:2008018. |
[15] |
A. K. Kapila, B. J. Matkowsky and A. van Harten, An asymptotic theory of deflagrations and detonations. I. The steady solutions, SIAM J. Appl. Math., 43 (1983), 491-519.
doi: 10.1137/0143032. |
[16] |
K. K. Kuo, "Principles of Combustion,'' Wiley, Hoboken (New Jersey), 2005. |
[17] |
S. B. Margolis and M. R. Baer, A singular-perturbation analysis of the burning-rate eigenvalue for a two-temperature model of deflagrations in confined porous energetic materials, SIAM J. Appl. Math., 62 (2001), 627-663.
doi: 10.1137/S0036139900377780. |
[18] |
J. Menkes, On the stability of a plane deflagration wave, Proc. Roy. Soc. London. Ser. A, 253 (1959), 380-389. |
[19] |
J. R. Mika and J. Banasiak, "Singularly Perturbed Evolution Equations with Applications to Kinetic Theory,'' World, Singapore, 1995. |
[20] |
I. Müller, Flame structure in ordinary and extended thermodynamics, in "Asymptotic Methods in Nonlinear Wave Phenomena'' (eds. T. Ruggeri and M. Sammartino), World, Singapore, (2007), 144-153.
doi: 10.1142/9789812708908_0013. |
[21] |
L. Pan and W. Sheng, The scalar Zeldovich-von Neumann-Doering combustion model (II) interactions of shock and deflagration, Nonlinear Analysis: Real World Applications, 10 (2009), 449-457.
doi: 10.1016/j.nonrwa.2007.10.006. |
[22] |
W. C. Sheng and D. C. Tan, Weak deflagration solutions to the simplest combustion model, Journal of Differential Equations, 107 (1994), 207-230.
doi: 10.1006/jdeq.1994.1009. |
[23] |
S. Takata and K. Aoki, Two-surface problems of a multicomponent mixture of vapors and non condensable gases in the continuum limit in the light of kinetic theory, Phys. Fluids, 11 (1999), 2743-2756.
doi: 10.1063/1.870133. |
[24] |
S. Takata, Kinetic theory analysis of the two-surface problem of a vapor-vapor mixture in the continuum limit, Phys. Fluids, 16 (2004), 2182-2198.
doi: 10.1063/1.1723464. |
[25] |
D. H. Wagner, Existence of deflagration waves: Connection to a degenerate critical point, in "Lecture Notes in Pure and Appl. Math.," 102, Dekker, New York, (1985), 187-197. |
[26] |
Y. Yoshizawa, Wave structures of chemically reacting gas by the kinetic theory of gases, in "Rarefied Gas Dynamics'' (ed. J.L. Potter), A.I.A.A., New York, (1977), 501-517. |
[27] |
P. Zhang and T. Zhang, The Riemann problem for scalar CJ-combustion model without convexity, Discrete and Cont. Dynamical Systems, 1 (1995), 195-206. |
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