Large time behavior and energy relaxation time limit of the solutions to an energy transport model in semiconductors

Journal of Mathematical Analysis and Applications

Volumn 312, Issue 2, 2005, Pages 596-619

  Chen, Li ^a   Hsiao, Ling ^b   Li, Yong ^a  

^a TSINGHUA UNIVERSITY   (China)

^b CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

Drift diffusion; Energy relaxation time limit; Energy transport; Entropy inequality; Large time behavior

Indexed keywords

EID: 27744532086     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2005.03.063     Document Type: Article

References (18)

1. N. Ben Abdallah P. Degond On a hierarchy of macroscopic models for semiconductor J. Math. Phys. 37 1996 3333-3383
2. N. Ben Abdallah P. Degond S. Génieys An energy-transport model for semiconductors derived from the Boltzmann equation J. Statist. Phys. 84 1996 205-231
3. D. Chen E. Kan U. Ravaioli C. Shu R. Dutton An improved energy transport model including nonparabolicity and non-Maxwellian distribution effects IEEE Electron Device Lett. 13 1992 26-28
4. L. Chen, L. Hsiao, Mixed boundary value problem of stationary energy transport model, preprint
5. L. Chen L. Hsiao Y. Li Strong solution to a kind of cross diffusion parabolic system Comm. Math. Sci. 1 2003 799-808
6. P. Degond S. Génieys A. Jüngel A steady-state system in nonequilibrium thermodynamics including thermal and electrical effects Math. Methods Appl. Sci. 21 1998 1399-1413
7. P. Degond S. Génieys A. Jüngel A system of parabolic equations in nonequilibrium thermodynamics including thermal and electrical effects J. Math. Pures Appl. 76 1997 991-1015
8. S. Génieys Energy transport model for a non degenerate semiconductor. Convergence of the Hilbert expansion in the linearized case Asymptot. Anal. 17 1998 279-308
9. I. Gasser R. Natalini The energy transport and the drift diffusion equations as relaxation limits of the hydrodynamic model for semiconductors Quart. Appl. Math. 57 1999 269-282
10. J.A. Griepentrog An application of the implicit function theorem to an energy model of the semiconductor theory Z. Angew. Math. Mech. 79 1999 43-51
11. L.K. Gu Second Order Parabolic Partial Differential Equations 1996 Xiamen Daxue Publishing House (in Chinese)
12. A. Jüngel Regularity and uniqueness of solutions to a parabolic system in nonequilibrium thermodynamics Nonlinear Anal. 41 2000 669-688
13. A. Jüngel Quasi-Hydrodynamic Semiconductor Equations 2001 Basel Boston
14. A. Jüngel, Macroscopic models for semiconductor devices. A review, preprint
15. O.A. Ladyzhenskaya V.A. Solonnikov N.N. Ural'tseva Linear and Quasilinear Equations of Parabolic Type 1968 American Mathematical Society Providence, RI
16. Y. Li L. Chen Global existence and asymptotic behavior of the solution to 1-D energy transport model for semiconductors J. Partial Differential Equations 15 4 2002 81-95
17. P.A. Markowich C.A. Ringhofer C. Schmeiser Semiconductors Equations 1990 Springer-Verlag Wien
18. p(0, T; B) Ann. Mat. Pura Appl. 146 1987 65-96