The three‐dimensional wigner‐poisson problem: Existence, uniqueness and approximation

Franco Brezzi*, Peter A. Markowich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

104 Scopus citations

Abstract

We prove the existence of a unique, global classical solution of the quantum Vlasov–Poisson problem posed on the phase space ℝ x3 × ℝ v3. The proof is based on a reformulation of the quantum Vlasov–Poisson problem as a system of countably many Schrödinger equations coupled to a Poisson equation for the potential. The Schrödinger‐Poisson problem is first analysed on a bounded domain in ℝ x3 and the solution of the whole‐space problem is then obtained by a limiting procedure in which the domains ‘tend’ to ℝ x3.

Original languageEnglish (US)
Pages (from-to)35-61
Number of pages27
JournalMathematical Methods in the Applied Sciences
Volume14
Issue number1
DOIs
StatePublished - 1991
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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