Periodic solutions to the Wigner-Poisson equation

Nonlinear Analysis, Theory, Methods and Applications

Volumn 26, Issue 3, 1996, Pages 551-563

  Lange, Horst ^a   Zweifel, P F ^b  

^a UNIVERSITY OF COLOGNE   (Germany)

^b VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

Galerkin method; Periodic solutions; Schr dinger Poisson systems; Wigner Poisson equation

Indexed keywords

EID: 0000937912     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0362-546X(94)00298-V     Document Type: Article

References (19)

1. BREZZI F. & MARKOWICH P., The three-dimensional Wigner-Poisson problem: existence, uniqueness and approximation, Math. meth. Appl. Sci. 14, 35-62 (1991).
2. ILLNER R., LANGE H. & ZWEIFEL P. F., Global existence, uniqueness and asymptotic behavior of the solutions of the Wigner-Poisson and Schrödinger-Poisson systems, Math. meth. Appl. Sci. 17, 349-376 (1994).
3. STEINRÜCK H., The Wigner-Poisson problem in a crystal, ZAMM 72, 93-102 (1992).
4. ARNOLD A. & NIER F, The two-dimensional Wigner-Poisson problem for an electron gas in the charge neutral case, Math. meth. Appl. Sci. 14, 595-613 (1991).
5. ARNOLD A. & MARKOWICH P.A., The periodic quantum Liouville-Poisson problem, Boll. Un. mat. Ital. 4-B, 449-484 (1990).
6. RAIMES S., The Wave Mechanics of Electrons in Metals. North-Holland, Amsterdam (1961).
7. BATT J. & REIN G., Global classical solutions of the periodic Vlasov-Poisson system in three dimensions, Preprint (1992).
8. BATT J. & REIN G., A rigorous stability result for the Vlasov-Poisson system in three dimensions, Preprint (1992).
9. ZWEIFEL P. F., The Wigner transform and the Wigner-Poisson system, Trans. theory stat. Phys. 22, 459-484 (1993).
10. BOHUN C. S., ILLNER R. & ZWEIFEL P. F., Some remarks on the Wigner transform and the Wigner-Poisson system, Matematiche XLVI, 429-438 (1991).
11. LANGE H. & ZWEIFEL P. F., Dissipation in Wigner-Poisson systems. J. math. Phys. 35, 1513-1521 (1994).
12. RUNGER G., Über ein Schrödinger-Poisson System. Ph.D. thesis, Mathematisches Institut, Univ. Köln (1989). KASTENHOLZ M., Endlichdimensionales Langzeitverhalten für ein Schrödinger-Diffusion-System, Ph.D. thesis, Mathematisches Institut, Univ. Köln (1991).
13. RUNGER G., Über ein Schrödinger-Poisson System. Ph.D. thesis, Mathematisches Institut, Univ. Köln (1989). KASTENHOLZ M., Endlichdimensionales Langzeitverhalten für ein Schrödinger-Diffusion-System, Ph.D. thesis, Mathematisches Institut, Univ. Köln (1991).
14. KASTENHOLZ M., LANGE H. & NIEDER D., Periodic solutions of nonlinear Schrödinger equations, Port. Math. 46, Fasc. Supl., 517-537 (1989).
15. ANTOINE J. P., Dirac formalism and symmetry problems in quantum mechanics. I. General Dirac formalism, J. math. Phys. 10, 53-69 (1969).
16. LADYZSHENSKAYA O. A. & URAL'TSEVA N. N., Linear and Quasilinear Equations (English Translation) p. 45. Academic Press, New York (1986).
17. LIONS J.-L., Quelques methodes de résolution des problemes aux limites non linéaires. Dunod, Paris (1969).
18. GRECO D., Nuove formole integrali di maggiorazione per le soluzioni di un'equazione lineare di tipo ellittio ed applicazioni alla teoria del potenziale, Rc. Mat. 5, 126-149 (1956).
19. GILBARG D. & TRUDINGER N. S., Elliptical Partial Differential Equations of Second Order. Springer, Berlin (1983).