Scaling limits in the 3-D Schrödinger-Poisson system

Applied Mathematics Letters

Volumn 10, Issue 5, 1997, Pages 61-65

  Lopez J L ^a   Soler, J ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

Asymptotic behaviour; Rescaling; Schr dinger Poisson

Indexed keywords

EID: 17444448101     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(97)00084-0     Document Type: Article

References (9)

1. P.A. Markowich, On the equivalence of the Schrödinger and the quantum Liouville equations, Math. Meth. in the Appl. Sci. 11, 459-469 (1989).
2. H. Steinrück, The one-dimensional Wigner-Poisson problem and its relation to the Schrödinger-Poisson problem, SIAM J. Math. Anal. 22, 957-972 (1991).
3. A. Arnold and F. Nier, The two-dimensional Wigner-Poisson problem for an electron gas in the charge neutral case, Math. Meth. in the Appl. Sci. 14 (4), 595-613 (1991).
4. F. Brezzi and P.A. Markowich, The three-dimensional Wigner-Poisson problem: Existence, uniqueness and approximation, Math. Meth. in the Appl. Sci. 14, 35-61 (1991).
5. R. Illner, P.F. Zweifel and H. Lange, Global existence, uniqueness and asymptotic behaviour of solutions of the Wigner-Poisson and Schrödinger-Poisson systems, Math. Meth. in the Appl. Sci. 17, 349-376 (1994).
6. 3 AS, (to appear).
7. S. Kamin and J.L. Vázquez, Fundamental solutions and asymptotic behaviour for the p-Laplacian equation, Rev. Mat. Iberoamericana 4, 339-354 (1988).
8. J.A. Carrillo, J. Soler and J.L. Vázquez, Asymptotic behaviour and self-similarity for the three dimensional Vlasov-Poisson-Fokker-Planck system, J. Func. Anal. 141, 99-132 (1996).
9. P.L. Lions and T. Paul, Sur les mesures de Wigner, Revista Matemática Iberoamericana 9, 553-618 (1993).