An infinite system of diffusion equations arising in transport theory: The coupled spherical harmonics expansion model

Mathematical Models and Methods in Applied Sciences

Volumn 11, Issue 5, 2001, Pages 903-932

  Degond, Pierre ^a  

^a CNRS   (France)

Author keywords

Boltzmann equation; Diffusion approximation; Diffusion equation; Fokker Planck equation; Spherical harmonics expansion

Indexed keywords

EID: 0035613321     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202501001173     Document Type: Article

References (27)

1. J. Banaciak, On a diffusion-kinetic equation arising in extended kinetic theory, Math. Methods Appl. Sci. 23 (2000) 1237-1256.
2. N. Ben Abdallah and P. Degond, On a hierarchy of macroscopic models for semiconductors, J. Math. Phys. 37 (1996) 3306-3333.
3. N. Ben Abdallah, P. Degond, P. Markowich and C. Schmeiser, High-field approximations of the Spherical Harmonics Expansion model for semiconductors, to appear in Z. Angew. Math. Phys.
4. E. Bringuier, Kinetic theory of high-field transport in semiconductors, Phys. Rev. B57 (1998) 2280-2285.
5. E. Bringuier, Nonequilibrium statistical mechanics of drifting particles, Phys. Rev. E61 (2000) 6351-6358.
6. C. Cercignani, R. Illner and M. Pulvirenti, The Mathematical Theory of Dilute Gases (Springer, 1994).
7. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge Univ. Press, 1958).
8. P. Degond, A model of near-wall conductivity and its application to plasma thrusters, SIAM J. Appl. Math. 58 (1998) 1138-1162.
9. P. Degond, Mathematical modelling of microelectronics semiconductor devices, in AMS/IP Studies in Advanced Mathematics, Vol. 15 (AMS and International Press, 2000), pp. 77-110.
10. P. Degond, "Transport of trapped particles in a surface potential", submitted.
11. P. Degond, A. Nouri and C. Schmeiser, Macroscopic models for ionization in the presence of strong electric fields, Transp. Theory Stat. Phys. 29 (2000) 551-561.
12. P. Degond and S. Mancini, Diffusion driven by collisions with the boundary, to appear in Asymptotic Anal.
13. P. Degond, V. Latocha, L. Garrigues and J. P. Boeuf, Electron transport in stationary plasma thrusters, Transp. Theory Stat. Phys. 27 (1998) 203-221.
14. S. R. de Groot and P. Mazur, Non-equilibrium Thermodynamics (Dover, 1984).
15. P. Dmitruk, A. Saul and L. Reyna, High electric field approximation in semiconductor devices, Appl. Math. Lett. 5 (1992) 99-102.
16. J. L. Delcroix and A. Bers, Physique des Plasmas (CNRS éditions, 1994).
17. J. D. Duderstadt and D. R. Martin, Transport Theory (Wiley, 1979).
18. H. Federer, Geometric Measure Theory (Springer, 1969).
19. A. Gnudi, D. Ventura, G. Baccarani and F. Odeh, Two-dimensional MOSFET simulation by means of a multidimensional spherical harmonic expansion of the Boltzmann transport equation, Solid State Electron. 36 (1993) 575-581.
20. F. Golse and F. Poupaud, Limite fluide des équations de Boltzmann des semiconducteurs pour une statistique de Fermi-Dirac, Asymptotic Anal. 6 (1992) 135-160.
21. N. A. Krall and A. W. Trivelpiece, Principles of Plasma Physics (McGraw-Hill, 1973).
22. P. A. Markowich, C. Ringhofer and C. Schmeiser, Semiconductor Equations (Springer, 1990).
23. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations (Springer, 1983).
24. G. C. Pomraning, The Equations of Radiation Hydrodynamics (Pergamon, 1973).
25. F. Poupaud, Diffusion approximation of the linear semiconductor equation: Analysis of boundary layers, Asymptotic Anal. 4 (1991) 293-317.
26. Yu. P. Raizer, Gas Discharge Physics (Springer, 1997).
27. C. Schmeiser and A. Zwirchmayr, Elastic and drift-diffusion limits of electron-phonon interaction in semiconductors, Math. Models Methods Appl. Sci. 8 (1998) 37-54.