On the periodic Wigner--Poisson--Fokker--Planck system
type: Item
instance of: scholarly article
title: On the periodic Wigner--Poisson--Fokker--Planck system
zbMATH Open document ID: 1014.35084
DOI: 10.1016/S0022-247X(02)00327-X
author: Elidon Dhamo
author: Anton Arnold
author: J. A. Carrillo
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-02-11T00:00:00Z
review text: The aim of this paper is the analysis of the coupled Wigner-Poisson-Fokker-Planck (WPFP) system in one dimension with periodic boundary conditions in the spatial direction. The existence and uniqueness of global classical solutions is analyzed. The main technical difficulty in the existence proof is to show that the quantum Fokker-Planck term is a semigroup-generator in a weighted \(L^2\)-space. The potential term is then a Lipschitz perturbation of it.
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 81Q05
zbMATH DE Number: 1866683
zbMATH Keywords: Wigner equation
zbMATH Keywords: Fokker-Planck equation
zbMATH Keywords: diffusive quantum systems
zbMATH Keywords: semigroup theory
reviewed by: L. Vázquez
MaRDI profile type: Publication
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full work available at URL: s0022-247x(02)00327-x
OpenAlex ID: W2005706853
description: scientific article; zbMATH DE number 1866683