Diffusion limit of a non-linear kinetic model without the detailed balance principle

Monatshefte fur Mathematik

Volumn 134, Issue 4, 2002, Pages 305-329

  Mellet, A ^a  

^a UNIVERSITÉ PAUL SABATIER   (France)

Author keywords

Asymptotic model; Boltzmann's equation; Chapman Enskog's method; Hilbert's expansion; Non linear diffusion equation; Pauli's exclusion principle; SHE model

Indexed keywords

EID: 0012862895     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s605-002-8265-1     Document Type: Article

References (31)

1. Bardos C, Santos R, Sentis R (1984) Diffusion approximation and computation of the critical size. Trans Amer Math Soc 284: 617-649
2. Ben Abdallah N, Chaker H (2001) The high field asymptotic for degenerate semiconductors. Math Models Methods Appl Sci (to appear)
3. Ben Abdallah N, Degond P (1996) On a hierarchy of macroscopic models for semiconductors. J Maths Phys 37: 3306-3333
4. Ben Abdallah N, Degond P, Mellet A, Poupaud F, Electron transport in semiconductor superlattices. Quarterly App Math (to appear)
5. Ben Abdallah N, Desvillettes L, Génieys S (2000) On the convergence of the Boltzmann equation for the semiconductors toward the Energy Transport model. J Stat Physics 98: 835-870
6. Bensoussan A, Lions JL, Papanicolaou G (1979) Boundary layers and homogenization of transport processes. Publ RIMS Kyoto Univ 15: 53-157
7. Brézis H (1983) Analyse Fonctionnelle, Théorie et Applications. Paris: Masson
8. Cercignani C (1998) The Boltzmann Equation and Its Applications. New York: Springer
9. Conwell EM (1967) High field electron transport in semiconductor. Solid Stat Phys Suppl 9
10. Degond P (2000) Mathematical modeling of microelectronics semiconductor devices. In: Hsiao Ling et al (eds) Some Current Topics on Nonlinear Conservation Laws. Providence, RI: Amer Math Soc
11. Degond P (1998) A model of near-wall conductivity and its application to plasma thrusters. SIAM J Appl Math 58: 1138-1162
12. Degond P, Goudon T, Poupaud F (2000) Diffusion limit for non homogeneous and non-microreversibles processes. Indiana U Math J 49: 1175-1198
13. Degond P, Mancini S (1999) Diffusion driven by collisions with boundary. Asymptotic Analysis 27: 47-74
14. Dmitruk P, Saul A, Reyna L (1992) High electric field approximation in semiconductor devices. Appl Math Letters 5: 99-102
15. E W., Homogenization of linear and non-linear transport equations. Comm Pure Appl Math 45: 301-326
16. Federer H (1969) Geometric Measure Theory. Berlin: Springer
17. Golse F, Poupaud F (1992) Limite fluide des équations de Boltzmann des semiconducteurs pour une statistique de Fermi-Dirac. Asymptotic Analysis 6: 135-160
18. Goudon T (2001) Equilibrium solutions for the Pauli operator. C R Acad Sci Paris, Ser I 330: 1035-1038
19. Goudon T, Mellet A (2001) Diffusion approximation in heterogeneous media. Asymptotic Analysis, (to appear)
20. Goudon T, Mellet A (2001) Non-linear diffusion equation asymptotics for the semiconductors Boltzmann equation with non-micro-detailed Pauli principle: the self-consistent case (in preparation)
21. Goudon T, Poupaud F, Approximation by homogenization and diffusion of kinetic equations. Comm Partial Diffs Equs (to appear)
22. Ladyzenskaya OA, Solonnikov VA, Ural'ceva NN (1968) Linear and Quasi-Linear Equation of Parabolic Type. Providence, RI: Amer Math Soc
23. Larsen EW, Keller JB (1974) Asymptotic solution of neutron transport problems for small mean free paths. J Math Phys 15: 75-81
24. Lions JL (1969) Quelques méthodes de résolution des problèmes aux limites non linéaires. Paris: Dunod
25. Markowich PA, Schmeiser C (1997) The drift-diffusion limit for electron-phonon interaction in semiconductors. Math Models Methods Appl Sci 7: 707-729
26. Markowich PA, Poupaud F, Schmeiser C (1995) Diffusion approximation of nonlinear electronphonon scattering mechanisms. RAIRO Model Math Anal Numer 29: 857-869
27. Poupaud F (1991) Diffusion approximation of the linear semiconductor Boltzmann equation: analysis of boundary layers. Asymptotic Analysis 4: 293-317
28. Poupaud F, Yamnahakki A (1995) Drift diffusion models for heterostructures in semiconductors. In: Marcati P, Markowich PA, Natalini P (eds) Mathematical Problems in Semiconductor Physics, pp 165-175. Harlow: Longman. (Pitman Res Notes Math)
29. Poupaud F (1990) On a system of non-linear Boltzmann equations of semiconductor physics. SIAM J Appl Math 50: 1593-1606
30. Rode DL (1975) Low-field electron transport. In: Willardson RK, Beer AC (eds) Semiconductors and Semi-metals, Vol 10 pp 1-52, New York: Academic Press
31. Schmeiser C (2000) Macroscopic models for almost elastic nonlinear electron-phonon interaction in semiconductors. SIAM J Appl Math 60: 109-120