High-field limit of the Vlasov-Poisson-Fokker-Planck system: A comparison of different perturbation methods

Mathematical Models and Methods in Applied Sciences

Volumn 11, Issue 8, 2001, Pages 1457-1468

  Bonilla, Luis L ^a   Soler, Juan S ^b  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^b UNIVERSITY OF GRANADA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035605221     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202501001410     Document Type: Article

References (11)

1. L. L. Bonilla, J. A. Carrillo and J. Soler, Asymptotic behaviour of the initial boundary value problem for the three-dimensional Vlasov-Poisson-Fokker-Planck system, SIAM J. Appl. Math. 57 (1997) 1343-1372.
2. J. Nieto, F. Poupaud and J. Soler, High-field limit for the Vlasov-Poisson-Fokker-Planck system, Arch. Rational Mech. Anal., to appear.
3. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge Univ. Press, 1970), 3rd edition.
4. C. Cercignani, The Boltzmann Equation and Its Applications (Springer, 1988).
5. F. Poupaud and J. Soler, Parabolic limit and stability of the Vlasov-Poisson-Fokker-Planck system, Math. Models Methods Appl. Sci. 10 (2000) 1027-1046.
6. L. L. Bonilla, C. J. Pérez Vicente and R. Spigler, Time-periodic phases in populations of nonlinearly coupled oscillators with bimodal frequency distributions, Physica D113 (1998) 79-97.
7. L. L. Bonilla, Chapman-Enskog method and synchronization of globally coupled oscillators, Phys. Rev. E62 (2000) 4862-4868.
8. J. Kevorkian and J. Cole, Multiple Scale and Singular Perturbation Methods (Springer, 1996).
9. G. Frosali, C. V. M. Van der Mee and S. L. Paveri-Fontana, Conditions for runaway phenomena in the kinetic theory of particle swarms, J. Math. Phys. 30 (1989) 1177-1186.
10. J. B. Keller, private communication.
11. G. B. Whitham, Linear and Nonlinear Waves (Wiley, 1974).