×

zbMATH — the first resource for mathematics

The two-dimensional Wigner-Poisson problem for an electron gas in the charge neutral case. (English) Zbl 0742.35078
Summary: We prove the global existence of a unique classical solution of the two- dimensional Wigner-Poisson problem by a reformulation as a system of countably many Schrödinger equations coupled to a Poisson equation. The charge neutrality of the system implies the boundedness of the electrostatic potential in two dimensions, which is an important ingredient for the proof.

MSC:
35S10 Initial value problems for PDEs with pseudodifferential operators
35K55 Nonlinear parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
47D03 Groups and semigroups of linear operators
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Brezzi, Math. Meth. in the Appl. Sci. 14 pp 35– (1991)
[2] and , private communication (1989).
[3] Kluksdahl, Phys. Rev. B 39 pp 7720– (1989)
[4] Markowich, Math. Meth. in the Appl. Sci. 11 pp 459– (1989)
[5] Markowich, ZAMM 69 pp 121– (1989)
[6] and , Semiconductor Equations, Springer, New York, 1990. · doi:10.1007/978-3-7091-6961-2
[7] Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983. · Zbl 0516.47023 · doi:10.1007/978-1-4612-5561-1
[8] and , Methods of Modern Mathematical Physics II: Fourier Analysis, Self-adjointness, Academic Press, New York, 1975. · Zbl 0308.47002
[9] ’The one-dimensional Wigner-Poisson problem and its relation to the Schrödinger-Poisson problem’, SIAM (1990) submitted.
[10] Tatarskii, Sov. Phys. 26 pp 311– (1983)
[11] Wigner, Phys. Rev. 40 pp 749– (1932)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.