Asymptotic behaviour of solutions of the hydrodynamic model of semiconductors

Royal Society of Edinburgh - Proceedings A

Volumn 132, Issue 2, 2002, Pages 359-378

  Li, Hailiang ^a,b   Markowich, Peter ^c   Mei, Ming ^d  

^a SISSA   (Italy)

^b INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^c UNIVERSITY OF VIENNA   (Austria)

^d VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036984263     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0308210500001670     Document Type: Conference Paper

References (36)

1. U. Ascher, P. A. Markowich and C. Schmeiser. A phase plane analysis of transonic solutions for the hydrodynamic semiconductor model. Math. Models Meth. Appl. Sci. 1 (1991), 347-376.
2. K. Bløtekjær. Transport equations for electrons in two-valley semiconductors. IEEE Trans. Electron Devices 17 (1970), 38-47.
3. G. Chen and D. Wang. Convergence of shock schemes for the compressible Euler-Poisson equations. Commun. Math. Phys. 179 (1996), 333-364.
4. G. Chen, J. Jerome and B. Zhang. Particle hydrodynamic moment models in biology and microelectronics: singular relaxation limits. Nonlin. Analysis 30 (1997), 233-244.
5. P. Degond and P. A. Markowich. On a one-dimensional steady-state hydrodynamic model. Appl. Math. Lett. 3 (1990), 25-29.
6. P. Degond and P. A. Markowich. A steady-state potential flow model for semiconductors. Ann. Math. Pure Appl. IV (1993), 87-98.
7. W. Fang and K. Ito. Steady-state solutions of a one-dimensional hydrodynamic model for semiconductors. J. Diff. Eqns 133 (1997), 224-244.
8. I. Gamba. Stationary transonic solutions of a one-dimensional hydrodynamic model for semiconductor Commun. PDEs 17 (1992), 553-577.
9. I. Gamba and C. S. Morawetz. A viscous approximation for a two-dimensional steady semi-conductor or transonic gas dynamic flow: existence theorem for potential flow. Commun. Pure Appl. Math. 49 (1996), 999-1049.
10. I. Gasser and R. Natalini. The energy transport and the drift diffusion equations as relaxation limits of the hydrodynamic model for semiconductors. Q. Appl. Math. 57 (1996), 269-282.
11. H. Hattori. Stability and instability of steady-state solutions for a hydrodynamic model of semiconductors. Proc. R. Soc. Edinb. A 127 (1997), 781-796.
12. H. Hattori and C. Zhu. Asymptotic behavior of the solutions to a non-isentropic hydrodynamic model of semiconductors. J. Diff. Eqns 144 (1998), 353-389.
13. L. Hsiao and H. L. Li. Shock reflection for the damped p-system. Q. Appl, Math. (In the press.)
14. L. Hsiao and T. Yang. Asymptotic of initial boundary value problems for hydrodynamic and drift diffusion models for semiconductors. J. Diff. Eqns 170 (2001), 472-493.
15. L. Hsiao and K. Zhang. The relaxation of the hydrodynamic model for semiconductors to drift diffusion equations. J. Diff. Eqns 165 (2000), 315-354.
16. L. Hsiao and K. Zhang. The global weak solution and relaxation limits of the initial boundary value problem to the bipolar hydrodynamic model for semiconductors. Math. Models Meth. Appl. Sci. 10 (2000), 1333-1361.
17. J. Jerome. Analysis of charge transport: a mathematical study of semiconductor devices (Springer, 1996).
18. J. Jerome and C. Shu. Energy transport systems for semiconductors: analysis and simulation. In World Congress of Nonlinear Analysis '92, Tampa, FL, vols I-IV, pp. 3835-3846 (Berlin: de Gruyter, 1996).
19. T. Luo, R. Natalini and Z. Xin. Large time behavior of the solutions to a hydrodynamic model for semiconductors. SIAM J. Appl. Math. 59 (1998), 810-830.
20. P. Marcati and M. Mei. Asymptotic convergence to steady-state solutions of the initial boundary value problem to a hydrodynamic model for semiconductors. Q. Appl. Math. 58 (2000), 763-784.
21. P. Marcati and R. Natalini, Weak solutions to a hydrodynamic model for semiconductors: the Cauchy problem. Proc. R. Soc. Edinb. A 125 (1995), 115-131.
22. P. Marcati and R. Natalini. Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation. Arch. Ration. Mech. Analysis 129 (1995), 129-145.
23. P. A. Markowich. The steady-state semiconductor device equations (Springer, 1986).
24. P. A. Markowich. On steady-state Euler-Poisson model for semiconductors, Z. Angew. Math. Phys. 62 (1991), 389-407.
25. P. A. Markowich and P. Pietra. A non-isentropic Euler-Poisson model for a collisionless plasma. Math. Meth. Appl. Sci. 16 (1993), 409-442.
26. P. A. Markowich and C. Schmeiser. The drift-diffusion limit for electron-phonon interaction in semiconductors. Math. Models Meth. Appl. Sci. 7 (1997), 707-729.
27. P. A. Markowich, C. Ringhofer and C. Schmeiser. Semiconductor equations (Springer, 1989).
28. F. Poupaud. On a system of nonlinear Boltzmann equations of semiconductor physics. SIAM J. Appl. Math. 50 (1990), 1593-1606.
29. F. Poupaud. Diffusion approximation of the linear semiconductor Boltzmann equation: analysis of boundary layer. Asymp. Analysis 4 (1991), 293-317.
30. F. Poupaud, M. Rascle and J.-P. Vila. Global solutions to the isothermal Euler-Poisson system with arbitrarily large data, J. Diff. Eqns 123 (1995), 93-121.
31. S. Selberherr. Analysis and simulation of semiconductor device equations (Springer, 1984),
32. L. Yeh. Subsonic solutions of hydrodynamic model for semiconductors. Math. Meth. Appl. Sci. 20 (1997), 1389-1410.
33. B. Zhang. Convergence of the Godunov scheme for a simplified one-dimensional hydrodynamic model for semiconductor devices. Commun. Math. Phys. 157 (1993), 1-22.
34. B. Zhang. On a local existence theorem for a simplified one-dimensional hydrodynamic model for semiconductor devices. SIAM J. Math. Analysis 25 (1994), 941-947,
35. K. Zhang. Global weak solutions of the Cauchy problem to a hydrodynamic model for semiconductors. J. PDEs 12 (1999) 369-383.
36. K. Zhang. Zero relaxation limit of global weak solutions of the Cauchy problem to a hydrodynamic model for semiconductors. J. Diff. Eqns 171 (2001), 251-293.