Well-posedness of the hydrodynamic model for semiconductors

Mathematical Methods in the Applied Sciences

Volumn 19, Issue 18, 1996, Pages 1489-1507

  Yeh, Li Ming ^a  

^a NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; HYDRODYNAMICS;

DIRICHLET CONDITIONS; QUASILINEAR ELLIPTIC PARABOLIC HYPERBOLIC SYSTEM;

SEMICONDUCTOR DEVICE MODELS;

EID: 0030379450     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1476(199612)19:18<1489::AID-MMA848>3.0.CO;2-X     Document Type: Article

References (17)

1. Adams, R. A., Sobolev Spaces, Aademic Press, New York, NY, 1975.
2. Baccarani, G. and Wordeman, M. R., An investigation of steady-state velocity overshoot effects in Si and GaAs devices, Solid State Electron, 28, 404-416 (1985)
3. Brezzi, F., Finite Element Handbook, McGraw-Hill, New York, 1987.
4. Gardner, C. L., Jerome, J. M. and Rose, D J., Numerical methods for the hydrodynamic device model: subsonic flow, IEEE Trans. Computer-Aided Des., 5, 501-507 (1989).
5. Gilbarg, D. and Trudinger, N. S., Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 2nd edn., 1983.
6. Majda, A., Compressible Fluid Flow and Systems of Conservations Laws in Several Space Dimensions, Springer, Berlin, Heidelberg, New York, 1984.
7. Markowich, P. A., On steady-state Euler-Poisson models for semiconductors, Z. Angew. Math. Phys., 42, 389-407 (1991).
8. Massey, F. and Rauch, J., Differentiability of solutions to hyperbolic initial boundary value problems, Trans. Amer. Math., 189, 303-318 (1974).
9. Metivier, G., Problemes mixtes non lineaires et stabilite des chocs multidimensionnels, Seminaire Bourbaki, 671, 37-53 (1986-87).
10. Mokrane, A., Problemes Mixtes Hyperboliques Non Lineaires, PhD thesis, Rennes University, France, 671, 37-53 (1987).
11. Odeh, F. and Rudan, M., Multi-dimensional discretization scheme for the hydrodynamic model of semiconductor devices, COMPEL, 3, 149-183 (1986).
12. Schochet, S., The compressible Euler equations in a bounded domain: existence of solutions and the incompressible limit, Comm. Math. Phys., 104, 49-75 (1986).
13. Thomann, E., Odeh, F., On the well-posedness of the two-dimensional hydrodynamic model for semiconductor devices, COMPEL, 9, 45-57 (1990).
14. Treves, F., Basic Linear Partial Differential Equations, Academic Press, New York, 1975.
15. Valli, A. and Zajaczkowski, W. M., Navier-Stokes equations for compressible fluids: global existence and qualitative properties of the solutions in the general case, Commun. Math. Phys., 103, 259-296 (1986).
16. Yeh, L. M., On a steady state Euler-Poisson model for semiconductors, accepted by Comm. P.D.E.
17. Zajaczkowski, W. M., Non-characteristic mixed problems for non-linear symmetric hyperbolic systems, Math. Methods in Appl. Sci., 11, 139-168 (1989).