Finite-time blow-up and variational approximation scheme for a Wigner-Fokker-Planck equation with a nonlocal perturbation

M.H. Duong

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Abstract

The paper is concerned with analysis of a Wigner-Fokker-Planck equation with a nonlocal perturbation that consists both conservative and dissipative as well as nonlinear non-local effects. We first show that the system has a finite-time blow-up phenomenon. We then introduce a variational steepest descent approximation scheme for the system. At each step, the scheme minimizes an energy functional with respect to the Kantorovich functional associated with a certain cost function which is inspired by the rate functional in the Freidlin-Wentzell theory of large deviations for the underlying stochastic system.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages16
Publication statusPublished - 2013

Publication series

NameCASA-report
Volume1313
ISSN (Print)0926-4507

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