The quantum hydrodynamic model for semiconductors in thermal equilibrium

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 48, Issue 1, 1997, Pages 45-59

  Gasser, Ingenuin ^a   Jüngel, Ansgar ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Classical limit; Existence; Quantum hydrodynamics; Thermal equilibrium; Uniqueness

Indexed keywords

EID: 0039768709     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00001469     Document Type: Article

References (11)

1. U. Ascher, J. Christiansen, and R. D. Russel, Collocation software for boundary value ODEs, Trans. Math. Soft. 7 (1981), 209-222.
2. F. Brezzi, I. Gasser, P.A. Markowich, and C. Schmeiser, Thermal equilibrium states of the quantum hydrodynamic model for semiconductors in one dimension, Appl. Math. Lett. 8 (1995), 47-52.
3. C.L. Gardner, The quantum hydrodynamic model for semiconductor devices, SIAM J. Appl. Math. 54 (1994), 409-427.
4. I. Gasser, P.A. Markowich, and C. Ringhofer, Closure conditions for classical and quantum moment hierachies in the small temperature limit, to appear in Transport Theory and Statist. Phys., 1996.
5. I. Gasser, P.A. Markowich, D. Schmidt, and A. Unterreiter, Macroscopic Theory of Charged Quantum Fluids. Proceedings of the Workshop on "Mathematical Problems in Semiconductor Physics", Rome 1995.
6. I. Gasser, P.A. Markowich, A. Unterreiter, Quantum Hydrodynamics. Proceedings of the SPARCH GDR Conference, St. Malo 1995.
7. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd Ed. Springer, Berlin 1983.
8. J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Paris 1969.
9. P. A. Markowich, The Stationary Semiconductor Device Equations. Springer, Wien 1986.
10. F. Pacard and A. Unterreiter, A variational analysis of the thermal equilibrium state of charged quantum fluids. To appear in Comm. in PDE, 1995.
11. A. Unterreiter, On the thermal equilibrium solution of a bipolar quantum hydrodynamic model. Submitted for publication, 1995.